'Hymie ...... knows way more than I in this field' - Oh no he doesn't; but I'll give you my two pennyworth anyway.
Although you can no longer buy old fashioned pumps, fitted with a conventional speed selector switch - modern smart pumps are available with speed control.
These smart pumps are expensive, take a look at Screwfix - their cheapest is £75 versus circa £35 for a conventional pump.
As The Builder says, virtually all standard central heating pumps are fitted with 1 1/2" BSP threaded connections at a set separation - therefore providing the pump body will fit within the available space (with the water flow in the correct direction), any pump should suffice.
Screwfix has a smart pump with a 6m head and seven speed settings (code 73917) for £129.99.
However to accommodate the pump within the confines of the boiler enclosure - many manufacturers opt for a bespoke pump with specially prepared fittings which mean it is not easily interchangeable. If such an arrangement is used in your boiler, replacing it will not be easy.
And from personal experience, swapping the pump head will not work.
Your cheapest option might be as The Builder suggests, fit a pump external to the boiler (powered and controlled from the original circuitry), but I would expect to pay closer to £250 given that around 1/2 of this cost will be the pump.
But before going to all this expense, The Builders suggestion of cutting the power to the pump (while the boiler is in full-swing) is a good idea – and should identify whether the pump is the culprit. But be prepared for the boiler to go into lock out due to the overheat stat operating.