Tricky!
Has your Dr explained why he won't prescribe gel? That's really your starting point.
From what I've read on forums, GPs seem reluctant on 2 accounts: they aren't familiar with it and lack the knowledge to prescribe a separate progestogen alongside (which is essential) or it's about cost. So you need a polite conversation to ask why! If he won't tell you or stonewalls you, you may have to be a bit more assertive and ask why certain drugs are not available from that practice. Worst case scenario - and I'm not saying do this-you could ask him for a private prescription so it doesn't cost the practice anything, and will cost you around £12-£15 a month for gel and the progesterone..
In Europe and especially France, gel is the main form of HRT.
You might want to talk to him about risk though being honest, your risk of a blood clot at 44 if you have no history of clots and aren't obese, is really, really low. It's more of an issue for women over 60 or who are unfit.
The other issue is dosage- pills are a higher dose to get the same benefits because a lot of the hormone is lost in digestion. So in theory you might be ok with 1mg of estrogen in gel or a patch but need a 2mg pill.
You aren't really supposed to alter the dose of gel on 'a bad flush day'. You need to build up a constant level in your system. The idea is to find the right level to control your symptoms as much as possible ( so anywhere from 90-100% of the time) and the best way to do this is by sticking with a dose for a few weeks before increasing or decreasing.
If you do manage to convince him, then you will need to use either Norethisterone or Utrogestan as the progesterone side of it, each month, or have a Mirena coil fitted.
Sorry if this sounds a bit like a lecture, but I've used it for 8 years! It was recommended by my meno consultant as the first and best choice.
The important thing is that you keep using HRT to at least 50-ish due to early meno.