A carer asked me a while ago, why every employer that she went to insisted that she repeated the same training course that she had done before.
All organisations that provide care services need to be registered with the Care Quality Commission (CQC). The CQC inspect all these organisations to ensure that they are complying with the laws and regulations that govern them. As part of this, they check to make sure that employers are training staff to do the job that they are employed to do, and keeping them up to date.
There are no specific lists of training courses that are required by the CQC, however most people would be expected to have been trained on Health & Safety and Safeguarding as a minimum. After that it would depend on the nature of the job role that you are doing as to what training you would need to have had.
The best thing a carer can do is to make sure that you get copies of any certificates to prove that you have completed any training courses, and to be prepared to re-take these courses each year.
Keep in mind that if your employer has paid for you to do a course as part of your employment with them, there is no automatic right for you to have that certificate. If however you have paid for the course, then you can expect to have the certificate. Most employers are reasonable, and if you ask nicely will be happy to let you have a copy of the certificate, even if they have paid for the course.
Obviously if you suddenly go and ask for all your certificates, then your employer can reasonably assume that you are going to be looking for another job, so probably best to try and get certificates as you complete each course.