Update on this. it took me a long time, as I was happy riding my good bike in all weathers- but I knew deep down that it isn't a good idea as I don't have the time to clean it thoroughly after riding regularly or the £ to replace the gearset if it's wrecked in a couple of years of riding in wet grit.
In the end I decided against doing it myself. Partly I don't trust myself with a new job and so don't want to spend on the tools and risk damaging it further, and partly as I discovered that actually there was a 2nd broken spoke (!) which I hadn't picked up on.
So in the end I took it to Happy Days, the social enterprise in Sowerby Bridge and left it with them. They found that they actually had a new wheel with a similar cassette and offered me that, so I went for that as the price was very reasonable indeed and I feel that my old wheel was halfway to knackered anyway. They let me have the tyre and tube that were on it too, so I'm really pleased. It needed doing but I needed to avoid a big expense.
I gave it a test yesterday and it all seems to work pretty well. The gears are grumbling a bit so I think it will take a few months for the chain to work into the new cassette properly but there isn't any slipping or issues like that.
Thanks everyone for the advice and Colin for the offer of your wheel too! Glad to have it sorted. It took me forever as I only had weekends to do it and those have been very busy.