Apologies for not replying sooner, but some of us have full time jobs and families, so can only drop in here to help when we have a few minutes spare.
Crikey, you dont have a lot of scope there by the look of things. Foul drainage appears to run along the rear, and getting to that isn't going to be straightforward in the slightest.
Realistically, I think you have 3 possible options, first is try and get a soakaway under the front driveway somewhere. I'd dig a trial hole if possible and do a percolation test, see what, (if any), chance you have of a soakaway working. Second possible, is to try and direct the water towards the road somehow, and let the Highway Gullies take it. (Not strictly allowed, but needs must, and you didn't realise it would flow that way...)
Third option would be to reroute the downpipe from the front, along the side of the house, to discharge either on the flat roof over the shower room or preferably into the rear gutter. Downside is, it'll look unsightly, and also depends on the drainage for the rear rainwater, if that's also going into a soakaway, then you'll overload it very quickly and end up with a flooded rear garden instead, so may need to look at rerouting that into the sewer.....