Fair Trade for British farmers (or is it supermarkets!)

Very often I am mystified by the term 'Fair Trade' as I am not really sure that it benefits the producers of the products that carry the logo. The idea is that the money we pay for any product we as consumers purchase which carries the 'Fair Trade' symbol, will go directly back to the producer of that product so that in poor countries, the producers and farmers receive a fair price for their goods.
If that works as it is supposed to, then I'm all for it. However, I have serious doubts because in many poorer countries the lion's share of the land is owned by large multi-million pound companies usually based outside that country and they employ local people to grow and pack the produce for them. Of course this ensures that many people have work and access to schooling, housing and hospitals that they would otherwise not be able to access.
In some countries, the farmers and producers are part of co-operatives that enable them to receive good market rates for their goods and that does help them in many ways.
What I would like to ask is, why is it that there is no 'Fair Trade' agreement for British farmers and producers, especially with the supermarkets? I am always amazed when I hear reports on the 'Farming Today' programme on the radio. It seems that the supermarkets can destroy a farmer's livelihood with the stroke of a pen while paying what they consider to be a 'fair price' at the same time ensuring that their profits increase. We already know that they will not accept any fruit or vegetable that is not uniform in size, shape or colour despite it being quite a normal occurrence in the natural world. After all, we are not all the same size, shape or colour so why should we expect our fruit and vegetables to be that way. Most people would welcome the opportunity to buy good produce that doesn't fall into these categories even if it is misshapen and covered in soil.
The biggest scandal of all at the moment is milk. Dairy farmers are giving up at an alarming rate due to the low price that they are currently being paid for their milk and if this problem is not addressed very soon, we will be importing most of our milk. This will mean that other products such as cheese, yoghurt and butter will also be made from imported milk. I for one, want my milk to come from British cows that have been grazing in British fields and cared for by British farmers - even if I do have to pay a bit more for it and providing that no extra goes into the supermarket shareholders' pockets!