In March I start three months of shared parental leave, which I can not wait for.
My wife has made some great new friends during her time on maternity leave, and she's been to several welcoming and fun groups, events and get togethers.
I'll be throwing myself into those as much as possible, and also wondered if there were any groups in the area aimed more at new dads? Any tips from SE23-based dads? I'm slightly nervous about showing up at baby sensory and being the only bloke there...

You probably won't be the only one there, but in the minority. There are often Dads, either doing a short period of paternity or a day or two a week. I asked similar questions when I started looking after my 1 year old son permanently, but could only really find a football meetup... and some occasional weekend groups which seemed to be timed for dads who are working all week. Always felt I wanted something different, as the 9-5 thing is quite different to evenings and weekends... Good luck.

I had some morning off and just went to either whatever playgroup was on, as you plan to do, or just took ours out as normal.

As above, Dad's were in the minority but not a complete rarity either, but I don't recall much Dad specific, and most 'support' or other groups, whilst often named or marketed as for mums would take dads also.

Enjoy your time!