By all means flush it out , its worth a try and might solve it . Rads are about £100 iirc , shouldnt take a garage no more than an hour to replace if you decide to do that . Someone else could advise what else you could do but just saying what happend to mine was very similar to whats happening to yours ...cheapest first option is replace the rubber seal on the header tank cap or cap as well in case its letting in air then next cheapest option is replace header tank if its suspect cracked . I went down many routes of elimination part by part until i almost gave up , then a kind member on here helped me out and since then ive had no issues
If the OP's car has suffered an oil cooler failure at some stage the radiator may be fouled with oil emulsion. Flushing with a non-foaming detergent should fix it.
My experience has been with a Carlton that had a leaking cooling system and had been topped up with tap water. Descaler strong enough to shift the scale is also strong enough to attack aluminium
so I eventually gave in and fitted a new radiator (which worked like a charm
).
My radiator seems to be shedding its cooling fins so I imagine I will need to replace it soon
. Best price I have found so far is about £200 on trade club, I would be pleased to find a source at £100.