Philippines is not a country for which TB X-Ray is needed for entry to the UK. I don't think you need to do any registration or medical checks in the UK.
However you can get your passport updated at the Philippines Embassy with your married name. You can do this by post and will get your passport back in about 2-3 days and the fee is £15. You need to provided self-addressed envelope.
It is advisable to find a suitable NHS practice where you can register. This will mean you can then get an appointment in case of illness. The practice will tell you if they advise any health checks etc.
If you intend to work you would need to apply for a National Insurance number.
Local Council should be notified of where you are living and if there has been a 25% Council Tax reduction for single occupant of address, this will be lost from date of arrival.
When you have got your passport updated it might be a good idea to open a bank account. Usually this can be kept dormant for no fee but check with bank.
Can't think of anything else needed in sunny England. Enjoy!
