How good is your GP? I found that, although mine were understanding, they really only have basic understanding of treating eczema. How old is your little one? I think the eczema nurse at St Thomas' Hospital explained that the younger they are when eczema started the more likely it is that food allergy could be causing it and if you are exclusively bf it's hard to work out what's causing it.
First major recommendation is to stop using fabric conditioner when washing clothes. Highly perfumed stuff is a major trigger. My daughters eczema really improved after this. Use a bath emollient like oilatum (2 capfuls in a bath), wash with a cream emollient like diprobase rather than soap (pat it on baby so you can see the cream then put him in the bath) and then pat dry and cover in an ointment (we use diprobase ointment - it comes in big tubs). Rub gently in direction that hair grows (so running down the leg, not up and down). Wash all clothes at 60 to kill dust mites which is another major trigger. I found stuff like johnsons baby cream etc too perfumed for DD1 and always brought out a reaction.
You will need steroid cream to work on any flare ups. GPs always get upset about the strength they will give you, normally trying to palm you off with 0.5% but you need minimum 1%. Possible stronger depending how bad (like eumovate). Use this in bursts when skin is bad eg morning and night for a week then just night for a week then every third day for a week. The idea is to blast the eczema and allow the skin to recover, then wean the skin off it. This is what dr fox told me. This horrifies gps and pharmacists!
Also people with eczema get hot easily and this also triggers it. Basically their skin is always trying to fix itself so the immune system is running at a heightened level. Don't overdress and in summer let them sleep in vest and nappy, thinner covers etc.
Do you think you an get a referral to see a dermatologist? I have a fact sheet given to me by the hospital. I would happily photocopy and send to you if you like. PM me your address if you would like one.
The good news is if you treat it properly in the first 7 years of life, you 're-educate' your skin to work better and eczema doesn't become such a horrid problem when you are older.
I'm sorry this is sooooo long and hope it helps.