I transferred my landline and broadband from BT to Plusnet, having used several comparison websites to see what was available in this rural location. I switched using Broadband Genie and got a £50 Amaz0n giftcard as a reward.
I'd been with BT for many years, and on the odd occasion I'd switched elsewhere I always went back to them. The last round of price increases took my payments to £65/month for a landline that I never use for outgoing calls, and fibre broadband but it's only to the 'box', a mile away in the village centre, so the broadband speed here at home is never going to be superfast. I pay about £7 a month to Plusnet, on an 18 month contract, and I paid the year's line rental in advance. Plusnet is owned by BT anyway, I still have the answering service 1571, caller display, everything is the same except the price.
I rang BT when they emailed the price increase and they offered to change my package to one saving just a few pounds a month. I rang them again when I got a firm price from Plusnet and they wouldn't budge further. Three days after I'd committed to Plusnet and BT had notice that I was leaving them, one of their retentions team rang me to discuss all the options, they still wouldn't have matched it but in any case it was too little, too late, and they'd had multiple opportunities to tempt me to stay. It's such a shame that the best deals are for new customers, not loyal ones.
Good luck OP, I'm sure you can do very much better than the package you're on at present.