The problem I have is cooler radiators the further they are from the central heating system, these are lower floor radiators and to the rear of the house.
I have bleed and radiators which were all OK.
I have tried to balance the radiators by carrying out the following actions.
Closed all radiators, turned system on slowly open the inlet valve on the furthest radiator until it started to heat up.
Work backwards on all radiators to the bathroom were the main system is.
Following this I then checked all radiators again, by this time the furthest away radiators were a lot cooler than the nearer ones.
Please any help will gladly accepted
Thank you.

Many possibilitys exist for this problem.

If your system was installed as a loop system the you might be out of luck since the last radiators always get the coldest water.

Depending upon you system you might be able to raise the water temperature of the boiler. This solves the problem most of the time BUT in some cases the water temp is already at its limit.

It could also be that the pump has lost some of its capability to move the volume of water you need to get the hot water to the end area. That means that the water is staying in the closest radiators to long and the radiator is extracting more than its share of heat allowing the first area of heat good but the further away areas get cooler water. The pump chamber/impeller could just be worn out.

Before you make any changes to your system I suggest you call in a TRUE boiler professional to see exactly what the problem is. This can only be done ON site in the home not on a problem posting board like here since we have no idea how the system is laid out or the accurate system pressures or temperatures. Volume of water needed and distance and height of the system.