I have two interviews lined up, but I'm concerned that stagnation of the economy could lead to redundancies in any organisation, and as the "new guy" I'd be the first out the door if it came to that. Is this a valid concern, and therefore should I think very carefully before handing in notice given the current situation - or am I being melodramatic?
You'd have to be naive or reckless to ignore the possibility - the economic situation is highly volatile at the moment and without wanting to sound like a doomsayer I think there's going to be a non-trivial amount of companies that are going to have to make cuts if not outright go under.
As the "new guy" you'd enjoy fewer protections than those with longer service (all other things being equal) since in the UK there's no requirement to pay out any redundancy pay below the two year mark and they could drop you with a minimum of fuss (no need to go through redundancy consultation periods etc).
That's not to say moving is always a bad idea - but you would be well advised to do as much due diligence as possible to ascertain the stability of the potential employer and the role. If they are hiring for a key position that has recently been vacated then that's likely to be more stable than a team that's expanding and creating new roles.
Look too at the industry sector the company is in: have they been adversely affected by recent events or are likely to? Or have they been experiencing a boom? I certainly wouldn't be looking to go into something in say an airline right now! Pharmaceuticals on the other hand...