Solved the problem after sleeping on it overnight. I'm passing the following on in case it might be useful to someone else one of these days.
I drained the pipework as far as I could, leaving a few feet of 15mm containing water - with the tee midway along.
Then connected up my Acquvac vacuum cleaner configured in wet mode, stuck the hose on the tap on the end of the circuit, opened the tap at the other end of the pipework, and sucked the water out.
Within a couple of minutes I had nearly-dry pipework which allowed me to break and remake the 15mm solder tee without problems.
I suppose a complete job would have seen me put a drain valve on this pipework for good measure. Didn't bother - now that I know my trusty Aquavac can do the business I don't need the drain valve :)