It is not really practical by car. It's a long way
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The best route from London to Eastbourne would be to take the A23 from London to just south/west of Croydon the A23 turns in to the A22 just north of Caterham and continues south into Eastbourne. Some of the towns on the way are East Grinstead,Uckfield and Polegate.
To drive it there the shortest route is to use the Hollyhead Ferry.
About 4 hours and 20 minutes depending on what route you take.
A car hire company in London might not let you take it out of the country. You would be best to hire one separately in Ireland.
You can find the best deals on car rental service in London, by simply searching on Google. Search London car rentals on Google and you will get the best deals on Every ride you book with. Multiple vehicle options are available to hire within your budget.
There are several used car dealers in London for prospective car buyers to visit. These locations include Mayrlebone Car Centre, McCarthy Cars, and Cargiant.
You can get information on car auctions in London online. Often they are also posted in public notices in newspapers so also check there. Try to find multiple car auctions for the best results.
The BEST car boot sale in London has to be BatterseaBoot on Sunday Afternoons. It's at Battersea Park School, Battersea Park Road, London SW11 5AP every Sunday, late start.
According the AA Route Planner (GB Edition) the distance is 53.7 miles, this will take about 1 hour and 31 minutes to drive, assuming you take the direct route and there are no stops, accidents, breakdowns or other hold ups en route.
there are various sites Where you can find car rentals in London such as: 1.www.europcar.com/London 2.www.holidaycars.com/London 3.www.carrentals.co.uk/car-hire/london-guide.html
the best route to take is to look up in the manual for the directions and follow them. otherwise with car stereos the best thing to do is take it to an installer who specializes in car stereo installation.