Linny, I very much understand your frustration, Ds had severe eczema and it was hell for months. I was also furious about GPs not sorting the condition sooner, at the HC not being enough, at not being able to find out what the hell was DS reacting to.... so, having been through all that I'm going to be totally honest with you.
It's terrible to see our children getting red, then itchy, then full of cuts caused by scratching and finally the skin weeping with infection, but unfortunately every child is different and eczema is different in each case, so you will need to keep trying different creams until you find "the one" that suits your baby.
The HC only helps to stop the inflamation (redness) before it evolves to a worse stage (mentioned above), it won't cure eczema, it only sorts a symptom. The only thing you can realistically control to prevent the redness (or flares) coming back after they have been cleared is to keep applying emollients. If the one you are using doesn't work try another and another until you find "the" one. My personal ranking of the creams I have tried is the following: Aqueous cream - E45, Hidrous cream, Diprobase, Lipikar Baume, Aveeno, Eucerin 10% Urea. Being Eucerin the stronger.
BAre in mind that until you find the right emollient for your baby you will need to apply any emollient she is on as many times as it is needed (when DS was at his worst we covered him in Diprobase at every nappy change, but once we changed to Eucerin we went from 8-9 times a day to 3). You can get Aveeno and Eucerin in Boots for around 7 or 8 pounds for a 200+ml bottle. If you can afford it, get a bottle and if it works, you can try to convince your GP to prescribe them, mine did.
One of the most frustrating things about eczema is that the baby may be covered in rashes and scratching his skin off but by the time you arrive to the GP it all has magically disapeared and then they think you are over reacting! (AAAARGGHHH!!!). My advice would be to take pictures of it for the doctor to see. But bare in mind that, as disturbing as they are, rashes are only a first grade eczema, and in those cases the best thing is to keep things simple (HC + emollient) and wait for it to improve, it certainly does in most cases.
DS only got refered to a NHS dermatologist after we took him to see a deramatologist privately who assesed the severity of DS's eczema. Even then, the first time I saw the NHS dermatologist she told me DS's eczema was not really that bad, but when I showed him DS's cot sheet covered in blood (he had weeping and bleeding patches from head to toe which became worse at night), I got a year pass to see a NHS dermatologist without the need to be refered by a GP.
In terms of products for the bath, DS responded better to Oilatum Plus (Regular Oilatum didn't help at all, nor did Balneum but, as with emollients, the fact that they didn't work for him , doesn't mean by anymeans that they have not been perfect for babies suffering of similar intensity eczema).
In terms of food, my first impulse was to blame the introduction of formula, so I started trying different ones (including soya formula, which, seeing things in retrospective, I regret very much as DS is now allergic to soya, and believe me, most things that come in packages contain it, even bread). So, I would follow the suggestions of the GP in terms of feeding.
Hope that helps (and that I have not crossposted, I have been writing this for 40min )
Keep posting