Market researcher Kantar WorldPanel said on Tuesday Tesco's share of the UK grocery market was 30.7 percent in the 12 weeks to April 15.
That represented an improvement on the 30.2 percent reported in the prior month, but was still down on the 30.9 percent reported in April 2011.
The January profit alert was Tesco's first in living memory.
Last month the world's third largest retailer parted company with the CEO of its UK business and last week it outlined a plan to revive its UK business by spending over 1 billion pounds ($1.6 billion) on more staff, better stores and online shopping.
Kantar said Tesco's year-on-year sales growth was 4.2 percent in the 12-week period, lagging market growth of 5 percent but an improvement on growth rates seen so far this year.
The market researcher said market growth of 5 percent was the highest since January 2010 but was mainly fuelled by food price inflation rather than real volume increases.
The discounters and Waitrose (the upmarket chain owned by John Lewis
Among the UK's top-four grocers, Wal-Mart Stores Inc's
Last month Sainsbury beat forecasts for fourth-quarter sales.
(This version of the story was corrected to remove reference to seven-year low of 29.7 percent in third paragraph)
($1 = 0.6213 British pounds)
(Editing by David Holmes)