If they are that rough I'd suggest going to a slightly wider slick like a Ritchey Tom Slick or Tioga City Slicker in 1.4 or 1.5 inch width respectively.

I've done all these options. Commuted on an older Trek 970 for about 5 years using Panaracer Pasela TG1.25. Sold that and bought a Speciallized Stumpjumper and then built up a set of XT hubs with Mavic Open Pro 700c rims to produce one of the first disc brake hybrids a year before Kona came out with the disc equipped Dr Dew for about 1/2 the price of my own solution (GRRRRRR ain't that always the way?). More recently my "grocery getter" errand bike is running the old Tioga City Slickers that I removed from the Trek in favour of the Paselas. Between all three options there's extremely little difference between the Pasela's in 26 inch and the current 700c tires on the Speciallized. If I had to call it I sort of wish I still had my Trek. It seemed to climb hills a hair more easily. As far as flat speed and ride quality goes it's a wash. The Tiogas currently on the heavier and more upright mountain bike roll amazingly well but I remember when I swapped to the Paselas from these on the Trek that there was a noticable difference in speed. But with that speed came a harsher ride and the desire to go around some of the rough stuff. But the height of the Paselas was such that I never had any issue with denting rims or any other such nonsense.

I spent a few days in the downtown core of London this spring on my first ever European holiday. If I had to ride the sort of roads I saw in Piccadily Circus and Trafalgar Square and the other roads around there and if the rest of the stuff is like that or similar to the roads I found up in Dundee in town I'd suggest sticking to the 1.5 inch tires. Especially since you're running without the "crutch" of a suspension fork to ease the shocks coming up into your hands. If you did go with 700c you'd likely end up with 28's or wider just so you could run with a little under 100psi to help soak up the hits. At that point you're just as well off with the 26'ers as far as speed goes.

Of course the grass is always greener on the other side, eh?