Will I be forced on to fibre broadband if I don't want or need it?

No. The PSTN phone switch-off itself doesn't force a particular broadband package on you — it's about how calls are carried. If at the time of your phone line switch you also choose to upgrade your broadband service, you should still be able to choose the broadband service that suits your needs and budget, even if they are both supplied by a different provider to your current one. If a provider implies otherwise, it's worth double-checking with an independent source like Ofcom or Citizens Advice.