A new law making it harder for some Commonwealth citizens to immigrate to Britain takes effect Aug. 1 over ob-jections from critics who say it is discriminatory and will break up families.

Under the law, male Commonwealth citizens living in Britain will have to prove they can financially support their families before relatives living abroad are allowed to join them.The law will require proof that the families have somewhere to live in Britain and that a marriage was not entered into primarily for immigration reasons.

The Aug. 1 start-up date for the new law, written by Prime Minister Margaret Thatcher's Conservative government, was announced Friday by the Home Office, which is responsible for immigration.

The opposition Labor Party opposed the law as it proceeded through Parliament but failed to stop it. The bill formally became law on May 10 but left it up to the government to announce when the new measures would come into force.

"This is a shameful betrayal of the promises given by successive Home Secretaries and will cause great misery and hardship," said Roy Hattersley, the deputy leader of the Labor Party. He said Labor would fight for immigration controls that respect family unity.

The government said the new law was necessary because it was being left with the responsibility of supporting families of immigrants who couldn't afford to do so themselves.

The government also charged that in some cases, marriages were entered into solely to permit people who would not otherwise be allowed in to come to Britain.