consider buying a new fridge. If it is a very expensive one you could consider trying to get it repaired, it might be carbon dust in the motor.
I would also pull it out away from the wall and look at the drip tray, it might be leaking water onto some electrical part. Unplug it and look for any evidence of trapped, chafed or damaged wires or connections. You can do that yourself at nil cost.
However there is also the possibility that you have a general amount of earth leakage in your house, and your fridge is causing just enough to tip it over the tripping point. This will need an electrician. If you take photos of your consumer unit, meter, incoming supply, and the various wires and cables between and around them, especially the green and yellow ones, you can post them on the "Electrics UK" forum here and say you get RCD nuisance tripping, there may be some other suggestions if there is evidence of electrical work required. Say how old your house and electrical installation are, and if you live in town or country, and if you have an overhead or underground supply.
Other sources of earth leakage that may be contributing to the tripping load are "watery" appliances and those with heaters. So see if the tripping stops when you unplug washing machine, kettle, coffee maker, dishwasher, garden sockets, shower pump, boiler, oven hot tub etc. Switch off the immersion heater and the boiler using the wall switch if they have no plug, but unplugging is better for everything else.
You can also buy an RCD adaptor (as used with lawn mowers) and plug your fridge, or any other suspect appliances, in through that. Sometimes they will trip faster than the one in the consumer unit, depending on its sensitivity, if so this will help you identify for sure where it is coming from. If it trips at exactly the same time, then it is probably that one appliance. If it does not trip, that appliance is more likely not the main cause of trouble. A more scientific test requires a qualified and well-eqipped electrician.