In the UK, what type of flexible conduit should I use for electrics in shed that run underground and emerge through the concrete base?
If you're just looking to get a power supply to the shed, you probably don't need to use conduit at all. Steel Wire Armoured (SWA -- roughly equivalent to jacketed/direct bury rated MC) cable is suited to being run underground and doesn't need to be in a conduit. Additional benefits are that it's more resistant to a stray spade trying to dig through it (though if you aim to bury deep enough, that shouldn't be a problem - general guidance is at least 450mm deep, but minimum 2 spades deep should be sufficient) and you don't need to mess about pulling cable through the conduit.

If you want to make it easy to replace the cable entering the shed (should you ever need to), you could use a piece of pipe / conduit / trunking to pass through the concrete base to allow the cable to be pulled easily through.