Private clinic transfers

Morning all. I just had my 3rd failed FET. My first attempt of an FET was Nov 2022, 2nd Sept 2023 and 3rd April 2024. As you can see, very long gaps between each, due to thin lining and slowness of clinic. I feel my clinic (NHS) is reluctant to do any tests as to why I keep getting failed transfers. My partner and I have discussed the 4th and if they say no to tests, to take our frozen embryos elsewhere to a private clinic that will suggest them and just pay. Has anyone ever done done this & can recommend private clinics in London. Please also bear in mind I am 41 in July, time really isnt on my side. Thank you.