Shailesh Vara, Conservative party MP for north-west Cambridgeshire, said providing easier access to the UK for Commonwealth nationals would send a "loud and clear" welcome message to them in a post-Brexit world.
He said was important to nurture the "strong and deep" links with the 52 countries of the Commonwealth, including India.
"As Britain leaves the European Union it is vital that we do all we can to build stronger relations with the rest of the world. In so doing we need to maximise our existing links with countries and in the case of the Commonwealth those links are very strong and deep, in so many ways.
"Britain remains a popular destination for Commonwealth citizens, both for business and non-business purposes and we should seriously consider making it easier for those people to enter our country.
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"Doing so would send a loud and clear message to the Commonwealth that we really do value them and it can only serve to make the UK's relations with the Commonwealth ever closer."
Vara's statement comes a day after it emerged that the recommendations in the letter sent to Home Secretary Amber Rudd are dueto be debated in Parliament on February 26.
In 2015, the last year for which figures are readily available, from Australia, Canada and India alone, Britain welcomed 2.2 million visitors who spent over 2 billion pounds.
"These three Commonwealth states are consistently found among the top five non-EEA (European Economic Area) nationalities arriving in the UK and travel for both business and pleasure.
However, while EU citizens are collecting their luggage or exchanging greetings with loved ones, our Commonwealth friends wait tirelessly in the 'All other passports' queue."
The group of 45 MPs suggest that a key starting point in the renewal of ties with Commonwealth partners should be a reconfiguring of the UK's border control system.
"Voters made it clear during the referendum that they wanted the country to take back control of immigration. This government will deliver on that by building an immigration system that works for everyone," the spokesperson said.
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