Flickering lights

A local electrician could provide you with an EICR report it is a bit like a mot certificate but for your house not a vehicle. That would be the best way forward

Likely to be lose connections somewhere. The amount of energy flowing is measured as amps. If the the connection is thin could be a weak flow. When the other room is turned on it pulls more current, so the other light is brighter. If you have a dimmer switch it may not be compatible with LEDs.

From your description this doesn’t sound like a lamp issue. When lights are dim, then start flickering when another room is switched on, that can indicate a loose neutral or high resistance connection somewhere on the lighting circuit or at the consumer unit. The fact another room has now started flickering suggests it may be a shared neutral or connection issue rather than a single fitting. I’d recommend having a qualified electrician investigate sooner rather than later, as loose connections can worsen over time. The fix is usually straightforward once the fault is located.

1, A shared Neutral 2, Different types of downlighters or bulbs 3, The Light switch/ dimmer incompatible 4, Loose connection 5, Low voltage There are multiple reasons it could happen and I have come across all of the above

Flickering Lights in different rooms Definitely looks like a broken / loose neutral somewhere on the lighting circuit I would trace the fault at The consumer unit Lighting circuit 6 amp then check each wall switch and ceiling rose One at a time This is a job for qualified electrician not home owner