Check the MCB. It's not supposed to happen ("if they trip, they are working"), but they can wear out or go faulty. I had one on an electric shower that kept tripping after you turned the shower off. The heat soak would trigger the thermal protection in the shower and the MCB would trip. I changed the shower, and all was good for six months, and then the same thing started happening again.
The MCB for the shower was much easier to trip with your fingers, and it was almost trembling on the edge of popping open. It had a little play in the switch, instead of being solidly in place like the others. The other MCBs in comparison felt quite solid and needed a proper nudge to get them to trip. I changed that particular MCB and all has been good since.
The easiest check would be to try the toaster in a socket on a different circuit/MCB, and if it doesn't trip, try changing the MCB on the faulty circuit. It's not a difficult or expensive job, but if you don't know what you are doing, you can kill yourself messing about in a consumer unit. Unless you have an isolator switch between the meter and the consumer unit, you do have mains live electricity in there. It's possible that you have several MCBs protected by a MCCB, and that's where the fault could be.
It's also possible that the bus bar on that MCB has not been installed correctly, and it's not giving a good connection, and that's causing the MCB to trip. It would just need reseating, but given a MCB costs a few pounds, it's worth replacing and making sure it's on the bus bar correctly.
If you're not sure about going into the consumer unit, then get an electrician in and tell him what's going on, and he'll diagnose it and be able to run checks on the cabling, MCB, as well as the toaster.
