Budgetting for Food in Europe!

Try to locate and go to the street food markets in those cities and buy produce from there which can be cheaper. You can prepare meals from that. Secondly, go away from the tourist areas, find mom and pop eateries where the locals eat and save money. Another option can be find restaurants that serve all you can eat buffet for a fixed price. You could probably spend around $100 a day or less for both on food if you do that.

You can certainly be frugal on $150 per couple per day, even in London and Paris. Londoners are not all wealthy bankers and members of the aristocracy so there are plenty of places to get a cheap meal. Many international cuisines can be cheap along with the ubiquitous fish and chips plus supermarket meal deals of a sandwich/salad, crisps, fruit and a drink. Markets with street food vendors can be a great place for excellent food at good prices. You just need to be prepared to eat away from the major attractions as that is where rental prices will be the highest and therefore affordable by the big chains or the expensive independents.

or get a famous english breakfast in a "greasy spoon" in London(it's so filling that you'll probably skip lunch!).

That's one advice I wouldn't recommend. The typical "greasy spoon" uses the cheapest ingredients and the quality is often very poor and cooked at questionable standards. There are good alternatives but as I'm rarely in London for breakfast I can't offer any recommendations. All I can say is that the chain Bill's does provide a good breakfast albeit at a price slightly higher than a greasy spoon offering but I'd rather pay £3/£4 more for something a bit more decent.

You can eat at any price point you are comfortable with, just as if you were traveling in the US. My observation has been that prices are generally about the same as in the US unless you are only going to high end places. Adjust accordingly as you go along. Its the unexpected little things that bleed you while traveling - an unplanned taxi, pay toilets, deodorant, newspapers, postage, candy bars, etc.

I see you're from the Olympic Peninsula. You probably know how much it costs for food in Seattle (or heck, even Port Townsend or Sequim). That's how much it costs to eat in any city. You can always find inexpensive food, anywhere. And you can find expensive, fancy, and yes overpriced food, anywhere. For the most expensive cities (London, Paris) you will need to make a little more effort to keep the costs towards the lower end of the scale, but there are countless cheap eats to be found anywhere, it just requires seeking out those places (well, Scandinavia is a bit more challenging...). Same as in the big city near you.

We could definitely survive on $150 a day and have some very nice meals. Here's some suggestions for breakfast and/ or lunch:
Pret-a-manger - a chain located throughout the UK and even Paris - good soups, sandwiches, etc - can eat in or take away.
Major department stores in Europe generally have one or more dining venues.

Many museums have quite decent restaurants.

For what it's worth, just a few suggestions for London and Amsterdam, that won't break the bank, decent food in attraction areas.

In London, although Londoners I'm sure think its touristy, I really like Cafe in the Crypt by Trafalgar Square. Never had a bad meal there, and the location is great.
https://www.stmartin-in-the-fields.org/visit/cafe-in-the-crypt/
In Amsterdam, Golden Choptsicks for Asian and a chain called Bagels and Beans. Love them both
http://www.goldenchopsticks.nl/en/
https://www.bagelsbeans.nl/nl

Are you "budgeting" to know how much money to have in your checking account for ATM withdrawals ? Or just to guesstimate how much the trip will cost ahead of time ?
We just spend as needed -- in accordance with our generally frugal style. €15 "menu" meals interspersed with picnics and snacks from the grocery store. Sometimes the hotel has an extra-cost breakfast buffet; we check out the offerings before agreeing to take the hotel breakfast -- if not, we carry instant coffee and cocoa packets and grab a croissant down the street.

First, remember that unlike accommodation, you don't pay for food twice. In other words, your hotel, apartment, hostel, etc in Europe comes on top of what you pay for rent or mortgage at home. But when you're eating in Europe, you're not buying food in the US. So, the only concern you have is the price difference between the US and where you are going in Europe.

This price difference can come in a few forms:

1) Are you eating more meals out than you do at home? I find that I do, because I don't have a fridge or kitchen, and because I treat myself to more meals out when traveling.

2) Are restaurants or groceries more expensive than at home for the equivalent items or experiences? Usually they are about the same, but of course there can be exceptions.

3) Are you going to fancier places than you do at home? As said above, you can find cheap or expensive places anywhere. If you are planning on fancier meals on vacation than you normally eat at home, there's nothing wrong with that (for many, it's a reason they travel), but you do have to budget for this.

If you are looking to be frugal, supermarkets are your friend. They have all kinds of grab and go items (salads, sandwiches, etc), so you don't need to have a kitchen or to "cook." Note that supermarkets in Amsterdam (at least the last time I was there) did not take credit cards - only Dutch debit cards or cash. Supermarkets are also fun to visit, to see all the large and small differences. For instance, look at the potato chips in London (called "crisps" there). You'll see some flavors we don't have (like prawn cocktail or roast chicken) and won't see some we take for granted (like ranch).

Rick's books also list restaurants with a price range (I don't think he lists actual prices any more, but look in the front of the book for the $-$$$$ decoder). You can always look online for the menus of the places that interest you, so you can get a sense of what things will cost.

For breakfast, I often get yogurt from a supermarket. Similarly, for dessert I'll get some fruit, even if I've had a restaurant meal (check the hours of the supermarkets near you if you're thinking of doing this after dinner). This frees up some money for fuller breakfasts or dinners once in a while.

And I agree that if you are able to spend $75 for food per person per day, you certainly can do very well without having to scrimp. You won't just be eating from the supermarket three times a day!

A specific tip for Budapest (although it has been 11 years since I was there): There's an all you can eat buffet called Trofea Grill Etterem, with multiple branches under several different managements. I know this sounds dire, but it's actually very good. The grilled squid is one dish I still remember! As a bonus, if you go to a branch outside the very center, you'll see lots of Hungarian families (I seemed to be the only tourist). Note that lunch is much cheaper than dinner, and weekdays are much cheaper than weekends. Here's the one I went to: https://trofeagrill.com/en/restaurants/zuglo-etterem/

If you stay in B&Bs breakfast is usually free. When we do places on our own with a rental car, we try to stay in a small hotel or B&B. If breakfast is expensive at the hotel, we find an inexpensive option nearby that has coffee and danish or rolls. if we had a big breakfast, we skip lunch and dinner is our only cost for the day.

On our 28 day self drive tour of Wales and England (no large cities) we averaged about 50-60 GBP per day ($70-$85 US).
In large cities, you will spend more. While in Britain, we sometimes ate in pubs and had a great dark beer instead of wine for dinner.

Scandanavia is a special place for high cost, as is Switzerland. Southern Europe is less expensive. I remember being surprised when the check came in Lisbon for our dinner. My beer was less than a Euro and the entire meal for 2 cost about 15 Euros.

England has Groupon! (As does France and the Netherlands!) We've bought Groupons for London before and I've already bought one for our upcoming trip in June. I always crosscheck the restaurants on Yelp or TripAdvisor to make sure it's a decent place. It's sort of nice to have a meal paid for (or mostly paid for) before the trip even begins. Not only will I get them for meals but for afternoon tea, tours, etc. I was able to use my regular Groupon account to buy the English ones. Not sure about France and the Netherlands... I watch for their frequent promo codes so I get the Groupon for even less. We're not backpackers either but one of the reasons we're able to travel so extensively is I'm a bargain hunter! :D

If you're going to eat at a greasy spoon find a place that also provides a complimentary coronary angioplasty.

In England, Marks and Spencer has stores with sandwiches at most Tube stations.