After turning on toilet tap, the radiator in next room gets hot

I would imagine you have a combination boiler which is sited close to the radiator you are referring to. It sounds like the diverter valve is letting by slightly causing the nearest radiator to boiler to warm up whenever a hot water demand is put on the boiler.

Hello, as OPTO Gas has said, the boiler's diverter valve will likely be 'passing' and leaking heat to the radiators when all heat should be going to the hot water's plate heat exchanger. It could do this while the hot water is in operation or it could do it after the hot water is finished when the boiler should be in 'pump overrun mode' and just whizzing heat round the boiler's own internal bypass to cool itself down. It's usually not a big job on modern condensing combi boilers to repair the diverter valve. There may be a cartridge or repair kit which means that the whole diverter valve doesn't need to be replaced. If the diverter internals are found to be black with sludge when removed then you may need to discuss a flush or chemical treatment with your Gas Safe Engineer who is doing the job. The tap - if a hot water pipe or a central heating pipe is physically touching a cold water pipe due to poor installation practices, it can transfer heat into the cold water pipe through conduction and you can get a few seconds of hot from a cold pipe believe it or not. It may be something like that. As for the pressure, the cold side of the tap should have more pressure than the hot as it doesn't need to go through the boiler and lose flow rate due to the boiler's hydraulic resistance which the hot water does. There may be an isolation valve underneath the tap which is not fully open or the braided hose underneath may be partially kinked/folded over. Hope this helps.