700c is 622mm and the 26" x 1-3/8" Raleigh rim is 590mm. That's a bigger wheel, not smaller so you will not need a longer-reach brake -the braking area of the rim will be closer to the top of the fork and wheelstays. You will need a brake that will have a shorter reach. In fact, it will be so much closer that you will need to lose the original fenders and replace them with a thin modern fender if any will fit at all (or just go without). If one is going with 700c they might as well go with new modern brakes as well. By the time you replace wheels, tires, tubes, brakes, cables (might as well do levers too at this point that match the leverage ratio of the new brakes) and fenders you've probably put more money into the bike than you could spend on a new bike -and ruined the whole character, feel, and value of a "vintage bike" in the process. But that is a personal decision.

As for "availability" is concerned, many LBS's are carrying at least one brand of 590mm tires as there are tons of these old bikes around. I'm not so worried about availability as I am about price and selection at a LBS (unless it is one of those fast-food LBS's that only carries the 20 most common parts which I wouldn't go to anyhow). And there is always Amazon. Tires show up at your front door in 5-6 days. I can personally deal with that wait as tires don't self-destruct in a day and (like many people on this list) I own more than one bike