The short answer is no.
As Daniel says in comments, 650c has a 571mm bead seat diameter (which is basically the rim diameter). Modern 26" wheels are 559mm BSD, so it's a chance you could find a suitable wheel in that size and replace your rear brake cailper with long reach ones. That would, however, cost £50 on top of the new wheel and leave you with a bike that's quite odd to ride.
Looking at online shops in Europe £150-£200 does seem like a reasonable price for a new-build wheel. I've used Starbike before, and they stock one 650c rim for €42, a cheap hub for €40 plus spokes and another €55 to build the wheel... you're looking at £150 at least.
eBay has a couple of 650c wheels for around £100, which is likely to be year cheapest option for a new wheel.
The actual cheap option is a second hand wheel, or a second hand bike. It's probably cheaper to buy a second hand bike, and this time get one with 700c wheels. The small frame bikes might look nicer with smaller wheels, but as you've found it is not worth the hassle when anything happens to the small wheels. I've seen skinny tyre touring bikes with 559 wheels, but I don't recall seeing a road bike or hybrid built like that. They might exist, I just haven't seen them.
I've helped smaller riders a number of times over the years and in my experience there are really only three wheel sizes that work: 406 (20"), 559 (26") and 622 (27"). Anything else will make tyres somewhat harder to find (you will end up buying online because your LBS won't stock more than one tyre in your size, and it will never be the tyre you want), and wheels with be a giant PITA to find. 406 wheel adult bikes might look a bit odd but you can get tyres and wheels for them easily.