If you want to stay with 27-in, Panaracer Paselas in 27 x 1 1/4 really are the bomb. I had been running mine at 70 psi even on hooked bead rims, just because they float so nicely, but after using
this site's calculator for tire pressure with the 28 mm tires on another bike and loving the results, I think I will try 62 psi in the rear tire and 51 psi up front on mine. Which is WELL within the range of what a straight-walled rim can manage.
I must respectfully disagree. I've owned lots of vintage bikes built for 27-in wheels, and usually if they have their stock brakes there will be the necessary 4 mm of brake reach needed to accommodate the switch from 630 to 622. The adjustment slots on Weinmann 999s (probably a 610 up front/750 in back per British conventions) are at least 10 mm long if not more. It was common enough practice to switch out between 27-in clinchers and 700C tubulars to warrant building bikes with a mid-slot spec for brake pads. Even a crappy Batavus Tour de l'Europe could accommodate that switch. Mid-70s Dawes Galaxy is the freaky twin from another mother to the Raleigh Super Course of that era and I bet it will work just fine with the smaller wheels.
If you have any doubt, though - before buying 700C wheels, just look at the slots in the brake arms. If you have 4 mm or more space to go down, you're fine. For that matter, you can sometimes substitute a narrower brake pad and cheat things down a bit that way, too.
The cassette hub will probably play nicely with 70s era parts, though you'll want a new chain. The only limits you may run into are how far out you can set the rear derailleur limit screws to handle a wider cog block and how much cable pull you get out of your levers. I used to shift a Campagnolo Olympus mtb derailleur over an 8-speed Campagnolo cassette hub with 70s SunTour barcons and it worked, but I had to have everything dialed in just so to get all 8 gears. The modern cog shapes and a modern chain on old derailleurs usually shift very nicely, though.