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Mr Farron, who is the MP for the South Lakes in Cumbria, said the average household speed in the area was just 10.9Mbps, compared to the national average of 17Mbps.
New figures from the consumer rights group Which? reveal that 1 in 4 people in Westmorland and Lonsdale have less than 4.0Mbps broadband connection.
Under the Government's Universal Service Obligation, 10Mbps is the minimum speed that anyone in the UK would be entitled to request by 2020.
The Cumbrian MP has tabled two parliamentary questions to the government.
The questions seek to establish what progress is being made towards the Universal Service Obligation, and whether BT will face financial penalties if the targets are not met.
Mr Farron said: "The fact that one in four people in the South Lakes have a broadband connection of less than 4Mbps is frankly not good enough.
"Many small businesses in rural areas like ours are finding it impossible to function without adequate broadband.
"The government's Universal Service Obligation target of 10Mbps is nowhere near ambitious enough."
Canada, which was a much larger and sparsely populated country than the UK, had a target of 50Mbps, said Mr Farron.
"The government must put in place measures which penalise BT if they fail to meet the targets."
A government representative is expected to respond to Mr Farron's questions over the coming weeks.
Meanwhile, the National Infrastructure Commission has warned that urgent investment is needed in the UK's broadband and mobile networks.
Increased broadband speeds could add £17bn to UK output by 2024, according to an NIC report.
The report says the UK’s digital economy is the largest of any G20 nation as a percentage of GDP.
But it warns that almost one in four rural premises lack a decent broadband service.
The UK lags behind other developed countries – such as the USA, Netherlands and Japan – for 4G and broadband speeds, it adds.
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