Excess drinking and partying over the millennium, combined with a lack of access to emergency contraception during the holiday season, are being blamed for a 20% rise in abortions by a family planning charity.

Marie Stopes International, which runs a network of clinics throughout the country, said the impact of Christmas and the new year was beginning to be seen in thousands of unwanted pregnancies.

The news came as MPs and peers urged improved access to NHS abortion services, after research showed more than a quarter of women having terminations in England and Wales had to pay for private treatment.

According to Marie Stopes, abortions always rise in the first four months of the year, but this year's figures were unprecedented. In January and February, 6,900 women had terminations at the charity's seven clinics in the UK, compared with 5,759 for the same period in 1999.

Its deputy chief executive, Helen Axby, said: "This increase could be the tip of the iceberg. We may just be seeing the first swath of women who missed their periods after the holiday season. Others, particularly teenagers who are sometimes less aware of their bodies, may not yet have realised they are pregnant."

Franca Tranza, a spokeswoman, said: "Looking to the future, there are a number of things the government could do, for example allowing emergency contraception to be sold over the counter."

Britain has the highest teenage pregnancy rate in western Europe, with more than 8,000 girls under 16 getting pregnant each year. About half of the pregnancies end in termination.

A report for the all-party parliamentary pro-choice group found that of the 46,000 women each year who have private abortions, almost half would have preferred NHS treatment but were either refused by their GP or found the waiting time too long.

Baroness Gould, the group's chairwoman, said: "It is shocking that more than 30 years after abortion was made legal, some women still have problems getting an abortion within the NHS."