You could start with the cheapest and easiest approach. Start by fitting a system filter on the return pipe next to the boiler, bale out all the mud from the feed and expansion tank in the loft, and add a chemical cleaner such as Sentinel X400, and run it through the system for the prescribed period. This may be hours or weeks depending on the product. I would avoid aggressive acidic cleaners. The day you add it, turn off all the radiators except one, then all except the next, for half an hour each, to maximimise the flow and help disturb the sediment. The system filter will trap the particles that have been loosened, so you need to start off by emptying it daily. When there is only a smear of sediment being trapped, empty it once a week, then double the period between empties each time there is not much dirt, until it is only once a year. Emptying the system filter is a DIY job, like emptying your vacuum cleaner bag or the filter on your washing machine.
At the end of the period specified for the cleaning chemical, drain and rinse the system until it comes out clean, then refill using a corrosion inhibiting chemical.
This simple approach will not be as effective as a Powerflush, but it will be hundreds of pounds cheaper, so is always worth trying first. The system filter will trap any circulating particles in future and prevent sediment building up into any new blockages.
If you are strong and fond of simple plumbing, take the radiators outside and hose them through to wash out the loose sediment. You will be amazed how much there is.
When you have cleaned it, put aside a weekend for balancing the radiators carefully and thoroughly. It is simple but not a ten-minute job.