Noisy system

Our central heating system has become very noisy.

The house is a large 1950's 5 bedroom house and has a fully pumped, vented system with four zones controlled by zone valves and hot water. In addition rooms without thermostats have thermostatic valves fitted.

The boiler is a Trianco 45/50 and the pump is a Grundfos 15 60 which was replaced about three years ago.

The system was installed by the previous owner in the late 80's or 90's.

The system appears to have no bypass valve, although I understand on older installations it was common to have a bathroom radiator as the first load and left permanently open.

In warmer weather this makes the bathroom much too hot and it tends to get turned off.

A further problem is that the system is now not capable of heating all the circuits at once although all the valves work correctly and any three will work.

My diagnosis is that the pump has failed due to lack of a suitable bypass.

Before investing in a new one, I am asking for member's views.
Does seem like a good time to fix it before it gets cold again!

I am aware the boiler is old and probably undersized and needs replacing (when cash flow allows)

Noises - can be boiling due to lack of circulation, or singing due to scale, etc.
Lack of circlulation is due to inadequate pump, bad balancing, sludge, jammed /wrongly set valves etc etc.
Hard to say from here.

A singing boiler? That's Susan Boyle-er isn't it?

Can anyone suggest an easy way to test the pump?

Scale is unlikely as the water is soft.

Other things suggested are reasonably likely but it seems sensible to start with the pump.