...in a day? If not, what is the minimum size of boat and minimum engine would I be looking at to do this, baring in mind my budget only stretches as far as 4-5k.
Should add that the boat I'm looking at does have a closed cabin.
50 HP, 19 feet, not built for speed: Cruising will be around 10 knots , maybe 15 tops, so you are looking at a 15-20 hour trip, weather permitting. I would allow 3 days, with plenty of safe ports on the way in case the weather blows up. Remember there are regulations governing the preparations you need for this sort of passage