Baskervill was born a slave in October 1863 in Mecklenburg County. He was the eldest of five children, all sons, of Britton Baskervill, a stonemason, and Sallie Baskervill. Neither of his parents could, but his father’s hard work enabled Baskervill to obtain an education, graduating first in 1883 from the Boydton Academic and Bible Institute, in Mecklenburg County, and then in 1885 from the Wayland Institute in Washington, D.C. He returned to Union Level, in the Flat Creek District of Mecklenburg County, and taught school, farmed, and served as a superintendent of the Sunday school at Bloom Hill Baptist Church.
At its September 26, 1887, convention at Boydton the Mecklenburg County Republican Party nominated Baskervill for the General Assembly. He owed his nomination to factional rivalries at home and to the manipulations of William Mahone, the powerful leader of the state Republican Party. African Americans held a majority among the county’s voters and after 1869 had consistently elected black Republicans—, , and incumbent —to the General Assembly. In 1887 Hamilton sought Mahone’s endorsement, as did William A. Jamieson, the white county clerk. Jones and John M. Sloan, a white native of Ohio whom Jamieson had replaced as county clerk, ensured Mahone’s enmity by campaigning against his domination of the party. At the convention Jamieson withdrew, probably at Mahone’s orders, and directed his delegates to support Baskervill. Despite Hamilton’s assertions to the contrary, Mahone apparently considered him too close to Congressman James Brady, another Mahone enemy, and after several ballots enough of Hamilton’s delegates switched to Baskervill to give him the nomination. Jones and Hamilton were said to be contemplating independent campaigns, but they stayed out of the race and Baskervill easily defeated the Democratic candidate.
In the General Assembly, Baskervill voted consistently with the outnumbered Republicans and served on the Committees on Privileges and Elections and on the Chesapeake and its Tributaries. By the time the session ended in March 1888, the congressional campaigns were heating up. Baskervill asked Mahone whether he supported the candidacy of John Mercer Langston in the eleven-county Fourth District. The answer soon was clear: Mahone obtained the Republican nomination for Richard Watson Arnold, a white ally, and prepared to defeat Langston’s independent candidacy. His decision further divided the Republicans in Mecklenburg County. Hamilton broke with Mahone to endorse Langston, who received overwhelming support from blacks in the county. Baskervill remained loyal to Mahone, and by the end of the campaign was desperately asking him for cash with which to purchase votes. Despite fraud throughout the district on the part of the Democrats, later documented in a congressional investigation, Langston carried Mecklenburg County by 376 votes and was ultimately seated as Virginia’s first African American congressman.
A year later the county’s Republicans remained divided and disaffected, but Hamilton managed to repair his relationship with Mahone sufficiently to receive the nomination to the General Assembly, and he subsequently won the election. Baskervill returned to teaching and farming. He probably already had tuberculosis when he contracted influenza in December 1891. Britton Baskervill remained ill until his death on April 25, 1892. He never married but was engaged to an unidentified woman from Richmond when he died. His younger brother William H. Baskervill honored his memory by naming his firstborn son after him.