Good morning out of a sunny South Africa.

I am two and 1/2 days in London.
I also want to see Scotland. Can one do a day trip to Scotland by train?
Any suggestions?

NO !!
Two and 1/2 days are less than enough to see London. But even you would have ten days in london you can not see scotland like a day trip from London. Eevn if by plane!

theoretically you <i>could</i> do Edinburgh as a day trip - if you take the sleeper train up, arriving in the early a.m. and take an early evening train back.

Otherwise it is 4+ plus hours each way on day trains so you spend nearly 9 hours just traveling between the two.

W/ only 2+ days in London you really don't have time for a day trip anywhere let alone all the way to Scotland.

2 1/2 days is barely enough time to scratch the surface of London - to spend 10 hours trekking back and forth to Edinburgh - which I think charming - but simply not worth the time out of the VERY few hours you have.

You could get a 2 day trip in by getting the sleeper up , hotel one night and sleeper back this would let you DO Edinburgh, BUT I agree with others you will not see much in such a short time