Ballpark figure for central heating work

Recently had to get a gas engineer out as our boiler stopped working. Turned out an internal filter was covered in gunk.

Gas engineer said we could probably do with either a chemical or pressure flush of the system/rads. One or two radiators did have cold spots on them. He also recommended fitting a magnet 'trap' under the boiler to catch iron debris.

The boiler is around 5 years old but the radiators could be getting on for 40 years old. All I do know for definite is we havent had new radiators in the 18 years we have lived here.

So, can someone explain to me the pro's and con's of pressure vs. chemical flush and some ballpark prices for each. Plus what should the magnet 'trap' fitting cost at the same time.

We live in north yorkshire on the edge of the Yorkshire Dales not far from the A1. House is a 4 bedroomed typical late 70's estate type home, radiators (9 total) 1 per room apart from living room. Boiler is old style, not a combi, with a hot water tank.

Thanks in advance for any advice