Prime Minister James Callaghan, faced with spreading strikes by government workers and the possibility of embarrassment in this week's home rule referendum in Scotland and Wales, told Britain tonight he would try nevertheless to keep his minority Labor Party government in power until October.

"That is the proper time for an election," Callaghan said in a nationally televised interview, referring to the legal requirement that new national elections be held by the end of the government's fifth year in office. "I think we ought to see it through."

The unusual hour-long, prime-time interview with two BBC correspondents was broadcast live from the prime minister's residence at 10 Downing Street. It marks the beginning of a critical period in Callaghan's struggle to avoid an election this spring. His party's popularity is at a low in public opinion polls.

The labor strife that plunged the Labor Party nearly 20 points behind the rival Conservative Party in the polls is continuing.

Callaghan thought his government had won a settlement last week giving an 11 percent wage increase to 1.1 million garbage collectors, hospital attendants, school janitors and other workers in low-paid local government "dirty jobs." But the leader of the National Union of Public Employes has recommended rejection of the settlement in a slow-moving ratification process going on this week. Selective strikes by these workers over the past several months have closed schools and left uncollected garbage rotting in the streets.

Ambulance drivers, who want their pay raised to equal that of police officers and firefighters, also have conducted selective strikes and threatened a complete stop-page that would idle all the nation's ambulances this Thursday.

The latest strike action, and perhaps the most embarrassing to Callaghan, began Friday when 300,000 national government civil servants walked off their jobs in Cabinet departments, airport control towers and customs offices. They virtually shut the government down for a day.

That one-day general strike has been followed this week by selected civil servant strikes that have shut down government computers that collect taxes, pay subsidy grants, regulate arms exports, and decode secret international messages.

None of these strikes, or preceding ones by truck drivers and railroad workers, has done more than inconvenience targeted parts of the population. This winter's strikes and wage settlements increasing workers' pay by an average of about 15 percent follow three years of relative labor calm and small wage increases that helped reduce inflation here from 30 percent to 8 percent last year.

But this winter's strikes and an expected increase in inflation from the higher wage settlements and little increase in national productivity has unsettled the country and made the Labor Party a likely loser in a national election held now.

Callaghan, who had lost patience with strikers and angered the civil servants with a House of Commons remark last week that their strike was "unnecessary and unjustifiable," smilingly evaded questions tonight about specific labor problems.

This surprised commentators who thought Callaghan would use the interview to show voters that he was getting tough with the unions.But he apparently came away from a weekend meeting with Labor candidates for Parliament fearing that he might be alienating too many of the Labor Party's traditional union supporters.

He did say a policy agreement reached recently between his government and the national trade union leadership obligated that leadership "to help get inflation down to 5 percent over a three-year period." Some of the current strikes however, have begun without leadership approval even before contracts at old wage rates have run out.

Callaghan's problems are compounded by his dependence on support in Parliament from regional minority party representatives to avoid losing a vote of confidence that would force an immediate election

He is likely to lose the support of three Welsh nationalist members of Parliament this week following the almost certain defeat in Thursday's referendum in Wales of the Labor government's proposal for limited home rule for Wales.

The support of 11 Scottish nationalist members of Parliament for the Labor government hinges on whether Scottish voters produce a big enough majority for home rule in a companion referendum there Thursday. Opinion polls show "yes" voters still outnumbering "no" voters in Scotland, the reverse of the situation in Wales.