Predictions are suggesting up to 6% interest rates by next year. 6% is going to cripple a lot of people. However it is still within the upper limit of what the OP thinks they can pay, so I would say to try and stop worrying too much.
I think because rates have been so low, the market couldn't easily cope with rates significantly higher than this.
As others have said there are steps that mortgage lenders have to take for anyone who can not afford the interest rate rises. The most obvious step would be to switch to an interest only mortgage. Its far from ideal, however it does provide more security than having to go into the rental market.
I think anyone looking at remortgaging soon would be wise to look at fixed rate mortgages. Its a gamble but it looks like the next few years are likely to be unstable financially and its hard to see rates going down in the medium term. Thats the exact thing thats spooking the lenders into dropping current mortgage deals.
I would also suggest that anyone who is in a position to overpay their mortgage now (not all mortgages allow it) would be wise to do so, to try and soften the blow later on. If you can increase your LTV you get better terms and interest rates when it comes to remortgaging, so if you can take yourself over an LTV threshold (every 5% of the value of your house makes a difference), not only are you reducing the amount you pay in compound interest at your current rate, you are also more likely to get a sligyhtly more favourable rate going forward. It might not seem a lot but even a 0.1% on compound interest over 5 years will add up.
We are fixed until next year, and I have to say that although we can afford it, its still concerning. My parents nearly lost their house in 1989 when interest rates went sky high and my Dad lost his job at the same time. Despite this, they did survive it and did eventually get back on track and didn't lose the house.
The biggest thing to remember: its not in the interests of lenders to repossess. If there are a lot of repossessions going on, banks stand to lose money and thats ultimately not in their interests.
The people who this will hit hardest isn't those who currently have mortgages on their own homes; its those people looking to get a new mortgage in the next few years. It will also chuff people trying to get mortgages on second homes/buy to lets and existing renters who get stuffed with their landlords passing on the cost. Thats where it gets particularly messy, due to there being less protection available.