Voters in Scotland and Wales turned out in apparently large numbers in late winter sonw and rain today to decide whether they want the limited home rule offered them by the British Parliament.

Counting of the ballots will not begin until Friday morning with the results expected by evening. This is only the second time that a referendum, has been held in Britain. The first, a national referendum in 1975, reaffirmed British membership in the European Common Market.

Scotland and Wales have been ruled, along with England, by the British Parliament since Wales was formally incorporated into England in 1536 and Scotland was merged into Great Britain by the act of union in 1707.

The home rule plans offered them would create Welsh and Scottish assemblies with authority over education, housing, land use, health and social welfare. The assemblies would not be able to raise taxes and only the Scottish assembly would be able to pass new laws.The British government also would have veto power over the assemblies' actions.

Welsh voters were expec ted to reject the assembly proposal when they marked their paper ballots, on which the question was written in both English and Welsh. This bilingualism was achieved under pressure from the Welsh-speaking minority and produced strong opposition to home rule among the English-speaking majority in Wales.

Scottish voters, however, were expected to approve the assembly, with the size of the "yes" majority remaining the critical question. If it equals 40 per cent of the total Scottish electorate, including those who stayed home today, the assembly will be created automatically and elections for it will be held later this year in Scotland.

If the "yes" vote is smaller than 40 percent, however, no matter how much larger it may be than the "no" vote, the home rule legislation requires Parliament to make the final decision. That vote in the House of Commons could be crucial for the minority Labor Party government of Prime Minister James Callaghan, who has depended on the support of Scottish and Welsh nationalists to stay in power.

Today's election came at a critical time for Callaghan, who wants to avoid having to call a new national election until October, near the end of his government's five-year term in office.