Places to stay with a family of 4

Budget minded and Uk is difficult in general.
However i have always enjoyed Premier Inn and Travelodge UK. Both very clean and reasonable rates.
Ck their websites to see if it works on your itin.

We stayed in this vrbo in London last summer and really loved it. The owner was so sweet and helpful!

http://vrbo.com/443666

It was in Belsize park, which was maybe 15-20 minute tube from downtown, but the tube stop was like a block from the flat so it didn't really bother us. Plus there were cute restaurants and an amazing bakery in "our neighborhood", and we felt so local. Really enjoyed our stay.

There was only 1 bedroom, and in the living room it has a fold out foam sofa bed, plus the window seat we used as a bed as well, and we did just fine. :)

I also know a great flat in case you are going to Glasgow!

Have a good trip!

We loved our stay in the Cotswolds and had a fabulous house! It maybe larger than you need, but it is in a quaint village, and has all the charm you would expect to find. Owner was wonderful VRBO Listing #455256ha

We stayed at the Travelodge while in London. It was very clean, nice, and room bigger than I expected. You do have to check because not all locations have occupancy for more than two, ours had quad rooms. We also had breakfast included, so it was nice to just go downstairs and eat and be on our way.

The good news is that most self catering (cottage) accommodation is geared to your requirements - 2bedrooms for a family of four.
You don't mention the length of your trip or your preferred mode of transport.
My initial thought would be the train to Bath, then a rental car for the Cotswolds, York and Scotland, before the train back to London from Glasgow or Edinburgh.

You could consider staying on a farm - providing you have a car!
http://www.cotswoldsfarmstay.co.uk
http://www.farmstay.co.uk

Wow. I am so thankful for the comments. I have been looking at the farm locations just wasn't sure, so I appreciate the recommendations. This will be a 16 day trip. I'm thinking the trickiest part will be finalizing our itinerary. As this will be my kids first trip I've asked them places that are important to them. They have heard me talk about living in Aberdeen so surprisingly they want to go there (interesting for two teens want to experience something their mother has talked about.) I love all of the countrysides, my husband the Lakes District. So we will most definitely need a car. We are flying in and out of Gatwick - I have never been through that airport, any suggestions for this crazy trip would truly be appreciated. I'm not usually a big planner for trips, because we enjoy just exploring where our car takes us. This trip will need to be a bit organized as I never thought we would be able to take our kids, and will most likely be the only trip like this we can take with them. I'm going to get to the links you have given. Thank you.

Unlike continental Europe, in the UK 16 and over is an adult. So if you have any child over 15 pretty much all hotels are out unless you can spring for 2 rooms.

Not sure if you live in a town served by Icelandair, but on this one airline you can do an open jaw into Gatwick home from Aberdeen stopping in Reykjavik each way.

In just 16 days you will be covering some territory pretty quickly ...
London (4)
Bath & Cotswolds (3)
York (2)
Edinburgh (3)
Highlands (2)
Aberdeen (2)

Open jaw flights with London and Aberdeen would be sensible.

In London, take a look at homestays through At Home in London - some of the hosts have kids, which might be fun for your two. I just took a quick look at their offerings - not many that would fit your needs in Zone 1, but a number in Zones 2/3, in places like Balham, Chiswick, Ealing... Feel free to send me a PM if you'd like more information. My teen daughter and I really enjoyed our stay with a hostess back in 2008 and I'll certainly look there on our next trip to London - here's hoping it is soon!

We're also a family of 4 with 2 teens and have been to England twice in the last 3 years. For our first trip, my kids were under 16, so we could stay at Premier Inns. Family rooms were simple, lacked charm, but economical. For our 2nd trip my older child was over 16, so we couldn't stay in Premier Inn family rooms, but Travelodges didn't have a similar age limit, so we could stay there at a very economical rate.

We prefer to be in one room. We did a mix of lodgings -- Travelodge, B&Bs or small hotels with a double and 2 twins (or bunk).

Finding places with room for 4 takes some work. I start with RS guide (he mentions Quads). Then I do some searches to see what else is available. Rooms for 4 are often pretty crowded, but we are out and about most of the time so room is mostly for sleeping.

Thanks again. Been having some good success today finding places that might work. Hope to have reservations made in the next couple of days.

Prior to booking anything, I think it would be wise to come back on here and state your intended route / locations for staying. This is because people will advise for or against what you have planned. Also, zoom down on Google Earth to check the locations of the places where you plan to stay.