I've just done a bit of research for you into pills - each combined pill contains oestrogen and progesterone in different doses, and slightly different variations of the hormones. According to the NHS website, Femodene is still available and comes with either 20mg or 30mg of an oestrogen called ethinylestradiol and 75mg of a progesterone called gestodene.
If that worked for you and assuming its not available any more, it seems like Loestrin would be an excellent substitute for two reasons:
1) The type of oestrogen is the same type as femodene, and you can get Loestrin in 20mg and 30mg versions too, just like the femodene.
2) Loestrin uses a different progesterone called norethisterone - this is often prescribed on its own purely to stop bleeding so should be well suited to helping you with the bleeding.
That's all good in theory of course, although theres no way to know until you try it. If that doesn't work, you could try microgynon which is the most popular pill in the UK because it's effective in controlling symptoms without too many side effects. I've also heard that Binovum is used in people with problematic bleeding because the hormone dose varies throughout the month. So there are a few options you could try.
If the bleeding is like a continuous period it suggests that your endometrium is very thick and storing a lot of blood - I believe the thickness of it is controlled by your FSH (follicle stimulating hormone) so its possible that this is somehow imbalanced and causing your womb lining to thicken too much. Have they ever noticed on an ultrasound that your womb lining is quite thick? It may not show though if your bleeding all the time.
If you think about it logically, your hormones work to thicken your womb lining and release an egg, then shed the lining if the egg isn't fertilised (in over simplified terms). This usually happens only once a month, and the lining sheds until its back to normal and the process starts again. If you're having a continuous period, that implies to me that there's a problem somewhere with your hormones either making the lining too thick, or not stopping the bleeding. Again, I'm not a doctor but it seems like a logical conclusion.
If I were you, I'd go back to your gp and ask for either Loestrin 20 or 30 depending on what dose of femodene worked for you. You could either ask for a series of hormone tests to be done and wait to start the pill until after this, or ask for a referral to an endocrinologist to investigate your hormone levels and take the pill while you wait. I'd also ask for some iron supplements. When you see your gynae, make sure they understand fully that the bleeding is consistent all the time and ask why they think you're bleeding all the time - they might have an answer that has eluded me that seems logical, but ask lots of questions.
If you've had children and don't want any more or definitely don't want them, you could look into endometrial ablation which can be very effective in reducing bleeding.
I hope this helps - let me know how you're getting on and make sure you're resting.