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Manually emptying condensate will only fix temporarily. Don't leave it disconnected as you may in effect allow the boiler to flue into the house. Depends on how you'e done it.
The metal pipe isn't the condensate it' the pressure relife valve pipe
I find it hard to believe that anything could be worse in Stafford than it is in Stoke.Snow worse in stafford the newcastle and stoke
Thanks @RikkiE28 is frozen condensate almost certainly. Try more hot water. But it could be somewhere awward to get at not knowing how the pipes run means it's hard to say.
Doubt baxi will come out as it won't be covered by warranty.