I've soldered 0.5mm before, but I'm probably not the best at it. Would probably help if you say whereabouts in the UK you are.
You could try a local phone repair shop - if they do their own repairs they'll generally have the equipment and skill to do it.
Alternatively, try a hackspace - most of them are reopening this week. At the London one we have an infra-red reflow oven that can be used (though ideally you'd want a stencil to apply solder paste).