Glasgow — The recent Soviet order for $15.3 million worth of sophisticated diving equipment from the Scots-based Seaforth Maritime Company of Aberdeen has raised hopes here that the Soviet Union will place further contracts for its expanding deep-sea oil drilling operations.
John Brown's engineering company has already supplied over $153 million worth of pumping equipment for the huge Siberian-European gas line, and it appears that the Soviets are interested in gaining from the diving experience of British companies engaged in deep North Sea oil recovery work.
(British divers from an Aberdeen-based consortium fairly recently raised millions of pounds' worth of gold from a Royal Navy warship sunk off northern Norway in World War II while en route from the Soviet Union with bullion paying for military aid.)
The British contract, which was gained against French and German competition, is with the Soviet Ministry of Gas. It provides for the training of about 12 Soviet divers at the underwater center at Fort Williams, in northwest Scotland.
Seaforth Maritime has been asked by the Soviets to quote for a second diving equipment order, part of a submersible system vessel being built for the Soviet Union in Singapore.
A Glasgow-based company has also received a $2.3 million order for engineering equipment from the Soviets.
A spokesman for Aberdeen's Seaforth Maritime has said that ''the North Sea is packed with experience. That same experience can be exported to countries all over the world.''
Seaforth's present contract is for deep-sea diving in the Barents Sea, but Norway is disputing Soviet claims to oil rights in an area that is sensitive to both countries.
Although Prime Minister Margaret Thatcher has continued to approve of British companies supplying equipment to the Soviets' mushrooming gas and oil industries , the United Kingdom's involvement in Barents Sea explorations could be an embarrassment to her NATO partner Norway.
Again, Mrs. Thatcher's statement during the recent general election that ''the Russians are our sworn enemies'' appears to place her in the same position as President Reagan in relation to the Soviet grain deals.
A possibly more perplexing problem for Prime Minister Thatcher is an unconfirmed story that the British company of Vickers may have built two small submarines for the Soviet Union of the kind suspected of entering Sweden's territorial waters. Vickers is known to have supplied two fishing research submersibles.
Against this background of Soviet-British trade and its political consequences, 2,000 trade unionists with Glasgow's Rolls-Royce engine company have refused to support management efforts to secure nuclear contracts for the US Navy's new Trident system. Workers at Rolls-Royce have consistently opposed nuclear contracts, even though it is known that the Glasgow engineering workers belong to a union that is moderate and whose leaders basically support NATO's defense policy.