It's a bit more complicated than some of the above posts.
You can't take the CCP and HRT.
You can take the mini pill in a dose that's also part of HRT.
You'd probably need to see a consultant privately for that as a GP is likely not to know about it. The dose is roughly 3 mini pills a day (I only know this as it was an option offered to me not for contraception.)
For younger women who are on the Pill, there are 2 brands that are more natural (the estrogen in them) called Qlaira and Zoely. Some women use these which aren't exactly HRT but are better than the older pills and closer to the estrogen in HRT. The estrogen in the Pill is actually stronger than HRT but it's not body identical.
Unlike a PP here, I prefer gel to patches. The bonus is that you can adjust the dose from a very low dose - even just half a pump- to as much as you need up to 4 pumps a day with little medical supervision - ie getting an appt with a GP, a new prescription for a different patch etc- and you don't have a visible patch stuck on your bum.
You don't actually get daily 'spikes' as the absorption is over 24 hours once you've applied it
It takes up to 3 months for estrogen levels to fall once you stop HRT which shows it's not like filling an empty glass every day (or getting a spike.)