Two new phone services are available in London, one for theaters, the other for dining.

The theater service, Theater Tonight, can often provide tickets for sell-out shows like "Miss Saigon" or "Phantom of the Opera."It operates from noon to 6 p.m. and visitors can buy same-night seats at box-office prices with a Visa card. There is no booking fee. London telephone: 753 0333.

Dining by Numbers, a 24-hour service, has current information on hundreds of London restaurants, grouped geographically, in central London, inner London and outer London, with separate phone numbers for each.

Callers specify the part of the city, type of cuisine and price category and receive a choice of restaurants.

The computer can connect the caller to the chosen restaurant to make a reservation.

Details about opening hours, credit cards honored, examples from the menu and atmosphere are also provided.

A card with a map showing which phone number covers which area is available free from Direct Dining, 29 Dean Street, London W1V 6LL; telephone 287 3287.

In general, the numbers are, for central London, 839 12345-1; inner, 839 12345-2, and outer, 839 12345-3. Calls are about 80 cents a minute weekdays from 9 a.m. to 6 p.m., and about 60 cents a minute at other times. Each inquiry takes three to four minutes, and can be made from Britain only.

---- Budapest expects a busy summer for tourism. Reservations dropped off during the Persian Gulf war, but hotel and tourism officials say that they are optimistic that normalcy - being completely booked - will return over the summer season.

At Ibusz, the Hungarian national travel bureau, a staff member who deals with finding accommodations for individual travelers said, "The city should be just as full this summer as last." She pointed out that Pope John Paul II is to visit Budapest in August, an event that is expected to produce crowds that will overtax the city's tourism facilities.

Since last summer, two new hotels, the Korona and the Helia, have opened; a third, the Aquincum, is scheduled to open this month. The old art nouveau Gresham Palace is being converted into a hotel, but is not expected to be ready for a year and a half or two.