Wales or Scotland from London?

We arrive in London on Wednesday and then have Friday and Saturday to travel and fly out on Sunday.

I assume you mean your Sunday flight is early and you need to be back in London Saturday night. That gives you only two days including travel. North of Scotland is much too far, as is Wales. You want somewhere you can get to in ½ day or less.

I suggest York. Lovely old city with walls, Minster (cathedral), old streets etc. Official tourist site: https://www.visityork.org/

Trains leave every 30 minutes from London Kings Cross, trip takes 2 hours by High Speed Train. Depending on when your conference ends on Thursday you may even be able to travel to York on Thursday evening.
Look up train times and buy tickets on: https://www.virgintrainseastcoast.com/
Early Feb is short notice, many of the trains have already sold out of the cheapest tickets. So buy your tickets ASAP.

Cardiff would be nice. You could drive or train it. Be there for a day and then on the way back Worcester. Or if you haven't done it yet, I would send you to Dover. I loved it there.

We have been to North and South Wales, as well as Scotland. Loved all these places. Wales is closer and you can take a train to Cardiff and see many castles nearby. Tenby is a wonderful seaside town.
Conway is great in N. Wales.

With only two days, I do like the York suggest. We stayed there three nights and loved York.

Here is my review of our trip and cruise to USA after.
28 days in Britain and Celebrity Eclipse home
https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139

These are great suggestions! We are leaning towards York but Cardiff sounds good too. Thank you all for taking the time to respond.

York would get my vote over Cardiff.

Please note that early February is often when we experience some of the worst winter weather and half an inch of snow brings the country and transport to a grinding halt! Many places have had snow or flooding this past week, so be prepared for your plans to change if we get any extreme weather.

Either York or Cardiff would be great. York has the awesome Shambles and a good market. Plus the Minster and the wall. Cardiff is a great shopping city, with funky Victorian shopping 'alleys' to wander with great small shops, and a good market at St. David's church. There is the castle right in the heart of downtown, too. Whichever you choose, could you possibly get a train late afternoon or evening on Thursday? That would help maximize your time.

Scotland is having frequent snow at the moment and North Wales is having its fair share. Given the time of year I'd recommend a City break. Cardiff is a great city but there is a big rugby match on in the city on 3rd Feb so,you probably won't get a hotel then if that is when you are travelling. If not, then a few points on the previous post in case you ask for directions. The shopping alleys are known as the arcades ( not a video game in sight!) and are lovely, the market is by St Johns church, the Castle is in the heart of the city centre and well worth a visit. There's also the national museum which is free and well worth a visit for its impressive collection of impressionist art. If Castles are your thing then swing by the 'fairy tale' castle just north of the city at Castle Coch. If you have enough time and the weather's not foul visit the open air museum at St Fagans.

Plus Cardiff is only 2 hours by train from London Paddington.