Seconded for Lebara, if your data usage requirements are moderate - we now all use it in our household. There are some links on
MSE which give you slightly better blagged deals.
Broadband deals without the CPI+ mid-contract price rises are getting harder to come by, and they aren't the cheap ones. It will probably be cheaper overall just accepting the rise and factoring it into the total cost.
I'd suggest Plusnet 40/10 FTTC: £23.99 per month (line rental included), 18 month contract, no activation fee. Even if inflation is 13% and it rises to £28 after 6 months, plus another £5-£6 for Lebara SIM, that's still much less than you're paying today.
I'm sure Plusnet were selling that at £22.99 a week or two ago, and with £70 cashback thrown in, so it's a shame you missed that. Prices do fluctuate and it's worth checking out for Black Friday type deals. However, since you've only 6 days left, it's a bit late for that now - paying one or two months at out-of-contract rates will likely wipe out any savings.
There are also 1-month contracts available from the likes of Pulse8 and Cuckoo I believe.