Last HEX will be 23:48 I believe, which should leave enough time for you to get it. LHR baggage arrivals are actually quite swift compared to many other airports. There should still be a few tube trains running from Paddington when you get there, although not with a lot of time to spare and will depend on what line and final destination you want. You can check here: http://www.lasttube.co.uk/

However, personally, I would get a cab that time of day rather. I would not expect long queues or waiting times. To go all the way to the City (which will be pretty quiet that time of night) will, as said above, be about 60-70 quid on tariff 3, depending on where exactly you need to go.