They are among 41 communities in the region which will be getting an initial grant from the Coastal Community Fund.
Both will have a chance to bid for up to a £50,000 share of a new £3 million Coastal Revival Fund to support or restore local heritage and facilities which benefit the wider community and the surrounding economy.
But their Conservative MP Ian Liddell-Grainger is warning any money allocated must be spent sensibly.
Ministers have approved a £90 million budget for the initiative over the coming years. The cash injection is aimed at helping bring jobs, growth and prosperity back to beach towns and cities.
Many of these have suffered economically in recent years, partly from a decline in traditional British seaside holidays, partly because of low wages in the hospitality sector and partly because low interest rates have limited the spending power of the hundreds of thousands of pensioners in seaside retirement homes.
But since its launch in 2012, the Coastal Communities Fund has already allocated nearly £119 million to 222 local infrastructure and economic projects across the country, helping to create almost 13,700 jobs and provide more than 10,280 training places and apprenticeships.
The extension of the scheme to 2020 with at least £90 million of new funding was announced in the Summer Budget.
A £1 million allocation has been made immediately to help set up new Coastal Community Teams which will bring together local business, councils and people to help coordinate regeneration projects in their area –and to formulate bids for further grants.
Bridgwater and West Somerset MP Mr Liddell-Grainger said the announcement by Coastal Communities Minister Mark Francois meant the Government was serious about regenerating some of the most picturesque, but economically-deprived parts of the South West.
“But the last thing I want to see is this money being squandered,” he said.
“I hope this will just be the start of significant investment in Minehead and Watchet and that both will in due course be bidding for further allocations from the fund.
“But any success in the process will depend on the quality of the bids and the nature of the projects for which funding is being sought.
“Both I and the Government will be watching progress very carefully. This money is intended to finance tangible schemes which will deliver long-term economic benefits – not grandiose vanity projects or short-term job creation.”