London/Scandinavia

The must see items are generally the must see items described in any good guide. So get a couple of good ones and starting reading. Borrow from your local library. We cannot write a guidebook for you. And Scandinavia and London is a huge area with vast diversity of things to see. Our preferred time to travel in mid-Sept to first of Nov because the weather is better and crowds are less. For Scandinavia it would be to July/Aug.

Is your trip going to include both London and Scandinavia? And nowhere else in Great Britain? And are you considering Denmark, Finland, Sweden, Norway, and/or Iceland? Planning on doing any skiing in early 2020, as the snow will be better than in summer of fall! In our April trip to Iceland, some parts of the country were not accessible yet by car, and some activities were also unavailable until the weather warmed up.

June-August. Gets cold and rains start around first of September.
Suggest you purchase a travel guide for Scandinavia. The place is deadly expensive, and the most reasonably priced way to travel is by cruise ship--by far.

You question is too broard to answer in a meaningfull way. I would suggest you get some guidebooks and start doing some research, then come back and ask more specific question. Otherwise you risk getting useless answers, such as the ridiculous idea that a cruise is the cheapest way to see Scandinavia.

If I were taking such a cruise, I would want the cruise to include Finland. Time-wise this cruise would be in early June, maybe the 2nd half of May at the earliest.

June is best unless you prefer September.

There is no best time that is the same time for everyone. I will go to London or Sweden anytime. However, my preference is: Northern Sweden is either December for the shortest day and possible Aurora Borealis or just before midsummer. Just before midsummer is good for the long days, nice weather, and pre-cruise people...although the cruise people do arrive the week before midsummer in Stockholm in my experience. Cruisers that I saw in Stockholm seemed to be self-absorbed and tended to monopolize people and places...not by the numbers but by their actions so I'd recommend avoiding their schedules if possible. YMMV

You need to decide your own priorities. I don't travel anywhere in Europe in summer unless I'm visiting locals.

Scandinavia is best in July/August. It's the period with the most reliably good weather.

One way to do both would be to take a cruise, some start in "London" (I believe actually Dover area) and go into the Baltic. I like a cruise for the area because the cities are relatively compact and were all built to face the Baltic. Lodging, food and transportation can be pretty pricey in the Baltic so a cruise can also be a very affordable option.

If not that, definitely fly into and around Scandinavia. Trains and cars are slow, inconvenient and expensive options.

With our ultimate destination being Norway, flying an airline that hubs through London offers a low (air travel) cost option of a multi-city stop in London before continuing to Oslo. A few days in London is a great way to adjust to time shift before reaching Norway.

My favorite time to visit Norway is the weeks preceeding Easter Week. Length of daylight hours are longer and day temperatures milder than mid-winter, ski trails are packed in and marked and the mountain lodges.hytte are open and staffed. And being ahead of Easter Week, the hills are alive but not overcrowded.

London is nice during the pre-Easter late winter. Temperatures are comfortable and not packed with tourist.

I am going to disagree with some of the above. I have been to both numerous times.

My favorite times in London are May and September. We have spent varying times from 1-3 weeks and enjoyed the weather, flowers, and long daylight hours in May, and in September there is the month-long Thames festival. Our early spring mid-summer visits have been more often marred by rain.

For Scandinavia, I have only been to Denmark and Norway, 6 times total. This included visits in May (3x), August (2x), and November. The May visits have been the most enjoyable, in part due to the Norway national holiday celebration on 17 May, but also because the weather has been for the most part very nice. In August it was beastly hot in Denmark (like 32 degrees C) and air-con is unusual there. On the same visit, we experienced a blizzard in Norway.

But of course "your mileage may vary". And if you want to get out and hike in Norway, it is still brown rather than green in the Norway mountain areas (and/or partially covered with snow). But the cities and towns were nice.

Had a beer in Norway, cost 8 Euros
Had a beer in Portugal, cost 1 Euro.

Great “food for thought”! And we don’t drink beer, and want to visit Denmark where my husband lived and studied 30 years ago, but thanks for the input 😊

That's a bit more specific. Personally my favorite months in Denmark are June and July, especially around midsommer when the sun never seem to set and you have the long bright evenings.
I can see on your profile that your husband studied architecture in Denmark, so he might be familiar with the Danish Star architect Bjarke Ingels and his firm Bjarke Ingels Group (BIG). You can see his projects on their rather cool website https://big.dk/#projects