Firstly, you only take the MRCP if you want to become a physician. You can take Part 1 after FY1, or as soon after that as you feel ready. Having passed Part 1 is an advantage for specialty applications, but the fail rate is pretty high. You can then take Part 2 written any time after Part 1, and PACES (the practical) any time up to 7 years after passing Part 1, but if you want to progress you need to have passed by the time you're applying for registrar (ST3) jobs. If you want to do anything other than medicine (i.e. surgery, paeds, anaesthetics...) you have to take the relevant membership exams for those specialties, which all have their own slightly different schedule.
If you don't get your first choice of specialty/core training, either you take up an offer of an alternative, take a non-training post and reapply next year, or leave the country. There are probably more complicated options, but that's the gist of it.