The forecast, which compares with some industry estimates of 10 million, assumes more than 20 per cent of the population will be using mobiles within five years. This is a rate so far achieved only by Sweden.
Britain is among the most advanced of the mobile markets, with penetration of more than 7 per cent, but lags the 10 per cent reached in the US. The rest of Europe has been hampered by lack of competition and is fighting to catch up. Dataquest's figures show that penetration is only 3.6 per cent in Germany and less than 2 per cent in France.
Dataquest also estimates that the number of mobile subscribers worldwide will increase almost five-fold to 251 million by 1999. The market for mobile services is expected to be worth $154bn by then, compared with $40bn at the end of last year.
The market for the telephones and related equipment is likely to be worth $34bn by the end of the decade, compared with $19bn last year.
A spokesman for Dataquest said: "There is a view that the market in leading countries will find a ceiling. I do not agree. I believe that the speed at which we attain penetration growth will depend on the regulations governing the industry and by the actions of the operators."
He said that Dataquest made no attempt to speculate over the market shares of individual players.
The UK market is dominated by Vodafone and Cellnet, with the newcomers Mercury One-2-One and Orange bringing up the rear. One-2-One, which is owned by Cable & Wireless and US West, recently underlined the boom in the sector by announcing a pounds 235m expansion of its network.
The investment will give it national coverage by the end of 1997, well ahead of the target date of the end of the decade.
The market has been buoyed by fierce price competition and by the more consumer-oriented approach taken by One-2-One and by Orange, which is part of Hutchison Whampoa of Hong Kong.
One-2-One caused shock waves by launching its service with free off-peak local calls, a concept which it has said will remain an important part of its strategy.