The money, announced by Culture Secretary Jeremy Hunt, is part of the Government's drive to ensure that 90% of homes and businesses have access to superfast broadband by 2015.
English counties will get £294 million and Scotland £68.8 million to help the one-third of households that are not expected to have superfast broadband made available by the private sector.
County councils and private enterprise partnerships will be put in charge of broadband rollouts in their areas, and will be required to draw up delivery plans and find match-funding from elsewhere.
It will be up to the Scottish Government how to use the money in Scotland.
The allocations come out of £530 million committed by Chancellor George Osborne to improving broadband access over the course of the parliament.
The Government wants the UK to have the best superfast network in Europe by 2015.
Mr Hunt said: "Fast broadband is absolutely vital to our economic growth, to delivering public services effectively, and to conducting our everyday lives.
"But some areas of the UK are missing out, with many rural and hard-to-reach communities suffering painfully slow internet connections or no coverage at all.
"We are not prepared to let some parts of our country get left behind in the digital age."
The Culture Secretary said councils and the Scottish Government had to "do their bit" to roll out broadband locally.
"I urge all those suffering the frustration of slow internet connections to make it clear to your local elected representatives that you expect them to do what is needed to access this investment and to deliver broadband to your community," he added.
These are the English allocations by county and local authorities:
:: Bedfordshire (Bedford, Central Bedfordshire, Luton): £1,060,000
:: Berkshire (Bracknell Forest, Reading, Slough, West Berkshire, Windsor and Maidenhead, Wokingham): £1,430,000
:: Buckinghamshire (Buckinghamshire, Milton Keynes): £2,100,000
:: Cambridgeshire (Cambridgeshire, Peterborough): £6,750,000
:: Cheshire (Cheshire East, Cheshire West and Chester, Halton, Warrington): £3,240,000
:: Cumbria (Cumbria): £17,130,000
:: Derbyshire (Derbyshire, Derby): £7,390,000
:: Devon and Somerset (Devon, Plymouth, Torbay, Somerset, North Somerset): £31,320,000
:: Dorset (Dorset, Bournemouth, Poole): £9,440,000
:: Durham (County Durham, Gateshead): £7,790,000
:: East Sussex (East Sussex, Brighton and Hove): £10,640,000
:: Essex (Essex, Southend-on-Sea, Thurrock): £6,460,000
:: Gloucestershire (Gloucestershire): £8,070,000
:: Greater Manchester (Bolton, Bury, Manchester, Oldham, Rochdale, Salford, Stockport, Tameside, Trafford, Wigan): £990,000
:: Hampshire and the Isle of Wight (Hampshire, Isle of Wight, Portsmouth, Southampton): £8,420,000
:: Herefordshire (County of Herefordshire): £6,350,000
:: Hertfordshire (Hertfordshire): £1,110,000
:: Humber (City Of Kingston upon Hull, East Riding of Yorkshire, North East Lincolnshire, North Lincolnshire): £8,540,000 (subject to revision)
:: Kent (Kent, Medway): £9,870,000
:: Lancashire (Lancashire, Blackburn with Darwen, Blackpool): £10,830,000
:: Leicestershire and Rutland (Leicestershire, Leicester, Rutland): £3,880,000
:: Lincolnshire (Lincolnshire): £14,310,000
:: Merseyside (Knowsley, Liverpool, St Helens, Sefton, Wirral): £5,460,000
:: Norfolk (Norfolk): £15,440,000
:: Northamptonshire (Northamptonshire): £4,080,000
:: Northumberland (Northumberland): £7,030,000
:: North Yorkshire (North Yorkshire, York): £17,840,000
:: Nottinghamshire (Nottinghamshire, Nottingham): £4,250,000
:: Oxfordshire (Oxfordshire): £3,860,000
:: Shropshire (Shropshire, Telford and Wrekin): £8,210,000
:: Staffordshire (Staffordshire, Stoke-on-Trent): £7,440,000
:: Suffolk (Suffolk): £11,680,000
:: Surrey (Surrey): £1,310,000
:: Tees Valley (Darlington, Hartlepool, Middlesbrough, Redcar and Cleveland, Stockton-on-Tees): £770,000
:: Tyne and Wear (Newcastle upon Tyne, North Tyneside, South Tyneside, Sunderland): £3,420,000
:: Warwickshire (Warwickshire, Coventry, Solihull): £4,070,000
:: West of England (Bath and North East Somerset, City of Bristol, South Gloucestershire): £1,430,000
:: West Midlands (Birmingham, Dudley, Sandwell, Walsall, Wolverhampton): £630,000
:: West Sussex (West Sussex): £6,260,000
:: West Yorkshire (Bradford, Calderdale, Kirklees, Leeds, Wakefield): £6,340,000
:: Wiltshire (Wiltshire, Swindon): £4,900,000
:: Worcestershire (Worcestershire): £3,350,000
Secretary of State for Scotland Michael Moore said the money is "absolutely essential" to Scotland.
Speaking on the BBC radio's Good Morning Scotland programme, he said: "We are absolutely determined to get the economy back on its feet and it is going to be a choppy period while we do that.
"The Government has got to focus all its efforts on ensuring that we provide individuals and businesses with the tools they need to get their business and their enterprises growing.
"Superfast broadband is something that our competitors elsewhere in Europe and the world are investing in heavily.
"It is our determination that we will ensure that by 2015 we will have the best superfast broadband service in Europe and that 90% of households and businesses will be able to access superfast broadband.
"In many rural areas we have got a real deficiency and that is where we want to target this money.
"If we look at the investment the private sector is already making, something like 40% of Scots already have access to superfast broadband through the investment BT and others are undertaking.
"What we are trying to ensure is that we get the investment to the other areas where the market doesn't necessarily provide and what we will do with this money, which we hope the Scottish Government will match, is ensure that with that and other funding we actually underpin private sector investment in the rural parts of Scotland."
PA
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