Yes, Ox and Finch is excellent.
In Edinburgh, Valvona and Crolla is something of an institution: a wine merchant/italian delicatessen where you can get anything from coffee and cake to a full meal. A high end option I always recommend is the tasting menu at the Scotch Malt Whisky Society rooms - 5 courses with either matched whiskies or matched wines, depending on your preference.
And at the other end of the scale, while deep-fried Mars Bars are something of a tourist cliché, a late night haggis supper (i.e. haggis and chips [fries]) can be a thing of beauty.
I don’t see any discussion of where in London you plan to stay. You will find cheaper hotels on the outskirts but that means more time spent travelling to the places you want to go. Getting back after a show for example.
On cruise forums, the Park Plaza in Westminster is seen as a good compromise between cost and convenience. The water taxi from the pier opposite to The Tower of London is a good way to travel and get a different view. Tourist hot spots like The Eye and the Tower get very busy, so early moning (well at opening time anyway) or evening can help to avoid the queues.
The tube (assuming they are not on strike) is usually the fastest way to get from A to B, but you see a lot more from the top deck of a bus. Whichever you use, public transport (once the commuters have got to where they are going) is excellent and cheap. You pay by tapping your credit/debit card.
We’ve been to London a few times, and are pretty comfortable with the Tube (and buses). We’re staying in a smallish hotel a block from the Earl’s Court station, where we’ve stayed before. It’s a tiny bit pricey, but since it’s on the Piccadilly line, it’s easy to get around, especially when we head out to Heathrow.
@SanVito and @Stanislaus, we’ll take your joint recommendation for Ox and Finch to heart. Definitely looks like a place we’d enjoy. Thanks for the other recommendations as well. Our list grows ever longer and our trip seems ever shorter!
Keep your eye on the strike situation …
I noticed those were happening this week. Will definitely keep an eye while we’re there. We only have 2 long(ish) rides planned–Edinburgh to York, and York to London. With luck, we won’t be traveling on strike days.
Last time we were rerouted by a train strike was 1988 in Italy. The direct Milan to Venice (we were staying in Padova) route was on strike, so we had to go via Bologna. It was a little inconvenient, but we were much younger and more adaptable.