A phone on a Talkmobile contract is likely to be locked to Talkmobile services (or possibly to those of Vodafone, who actually own Talkmobile). So you might have to pay to get your phone unlocked in order to use it with a different provider. (Almost every street market seems to have a stall where you can get it done for a reasonable price).
With such low usage, there's probably little point getting another contract. A PAYG SIM might be better for you. Asda Mobile can provide you with a free SIM. You only need to make one chargeable call every 180 days to keep the service active. If you buy 'ordinary' credit (rather than 'bundles', which you don't need) it doesn't expire at the end of a set period. Calls cost just 8p per minute (without 'bundles'). So just £10 credit would be enough to get you a couple of 5 minute calls per month (which is all you seem to need) for an entire year. (Indeed, based upon your past usage, you might even get away with spending just a fiver per year).