sweeper,
A Power Flush (performed the way Agile states), sounds like the solution to me. Agile and any other reputable firm will take each rad off in turn and flush it out as well as the system. That way they will identify where any blockage may be and either shift it or even replace a section of pipework if required (which would normally incur an extra charge).
Try Softus' recommendation first:
'shut off all rads, then start at the top of the house and remove each one in turn, opening the valves to run water through the pipework (or find that it doesn't), and flushing the rad out in the garden'.
You may find it useful to buy a 'Washing Machine Tap'. The kind you might have under your sink. Attach a length of hose to the tap using a short length of copper pipe and a jubilee clip. Run the hose to a drain outside. Now drain your first rad down. Once it is drained you will find that the other end of the Washing Machine Tap (attached to your hose) should screw onto the radiator. Once you've attached it, open the other radiator valve and allow water to run for a while. If water fails to run... you've found a blockage to that area.
If you haven't guessed yet, the Hose is used to save you having to fill countless amounts of buckets with the water you run through the rad. Repeat the process for each rad and remember to flush the rads out well (a friend with a separate hose to flush out the rads and reconnect them while you work on the next part of the system is useful here... A crate of Bud may also be required
). Once you've run a decent amount of water through a section, remember to close BOTH rad valves before you remove the rad for flushing.
As I said, it'll take you a good few hours, you may even need to perform the whole job over a few days depending on your level of competence, confidence and your ability to con a friend into helping you
but if you solve the problem great! if not, then what have you lost apart from your own time and your mate's... oh, and a crate of bud!
You will also find several old rags/towels come in VERY handy for mopping up any spillages/leaks.
Hope that helps. Happy New Year.
edit: Forgot to say, make sure you switch OFF the boiler.