Alexander Yakovenko said the relaxation of visa restrictions would provide better trade and tourism for both countries.
During a speech at the Royal United Services Institute (Rusi), Mr Yakovenko said visa regulations must be “simplified” to strengthen the ties between the countries.
“We want more British people to come to Russia for business for travel, for tourism,” he said.
“We expect people to come, especially the Russian speaking population to develop the economic sphere in our country.
“We have a policy to ease the visa regime with all the countries of the world. Now we have a visa-free regime with almost 100 countries and this is going quite well.
“I remember five years ago when we abolished the visa regime with Israel – the business jumped by five times almost in one year. Now we have 12 jumbo planes every day to Tel Aviv from Moscow.”
For Russians to gain a visa to enter Britain it could take weeks, but if they want to enter EU countries which are part of the Schengen agreement, it takes just days.
Under the Schengen Agreement, citizens in 26 European Union nations are allowed to travel across borders without having their passports checked.
To avoid lengthy visa applications, business men and women from Britain often meet their Russian counterparts in Paris.
Mr Yakovenko said that in the next two years Russia hopes to have a visa-free regime with countries in the Schengen zone.