Born in Fenton, Stoke-on-Trent, Allen attended Hanley High School. Despite playing for the school rugby team, his preferred sport was football, and he turned out for his local Boys' Brigade team and later, Wellington Scouts. He then moved on to Northwood Mission where he played at outside-right, alongside Bill McGarry and Basil Hayward, who would later become his team-mates at Port Vale. Allen scored 57 goals for the Mission in the 1943–44 season.
Allen signed amateur forms with Port Vale in December 1944. He made his full debut on 2 April 1945 in a 2–2 draw against Wrexham in the Football League North, playing at outside-right and laying on one of Vale's goals. He scored his first goal for the club in a 4–3 win against Norwich City in August 1945, and in March 1946 signed as a part-time professional, for which he received a £10 signing-on fee. The 1946-47 season was the first full season of competitive football in England following the end of the Second World War; Allen made his Football League debut on 7 September 1946 in a 2–1 defeat to Exeter City. Due to his national service commitments, he only made 18 appearances during that season, scoring five goals.
Allen joined the Royal Air Force early in 1947 and represented their football team on several occasions. He was demobbed on 1 June 1949.
Allen was transferred to West Bromwich Albion on 2 March 1950 for £20,000, a club record fee for Albion at the time. He scored on his debut two days later to secure a 1–1 draw against Wolverhampton Wanderers in a Division One match. The attendance of 60,945 remains a record for a league game at The Hawthorns. Though only 5 foot 8 inch (1.73 m) and barely 11 stone (70 kg), he emerged as a talented striker, helping to define the modern role of target man.
Allen scored against former club Port Vale in the FA Cup semi-final and then scored twice in the 1954 final, which Albion won. He was First Division top scorer in 1954-55 with 27 goals.After 458 games and 234 goals with West Brom, he moved to Crystal Palace F.C. in 1961.
Allen made his England debut at the age of 23, in a 3–0 friendly win against Switzerland in Zurich on 28 May 1952. He had to wait almost two years for his second cap, which came against Scotland on 3 April 1954, the same day that his club West Bromwich Albion were playing rivals Wolverhampton Wanderers in a vital Division One match. Allen scored with a header in the second half to help England beat the Scots 4–2 in the match at Hampden Park, and also had another headed goal disallowed. He was included in England's initial squad for the 1954 World Cup, but did not make the final travelling party. He nevertheless earned three further caps, the last of which was against West Germany on 1 December 1954. Allen scored from six yards out in a 3–1 Wembley win against the World champions. On his lack of England caps, Allen himself said, "No two people see the game the same way and everyone is entitled to his own judgement".
In addition to scoring two goals in five full internationals, he also appeared twice for the England B team; both matches took place in 1954. He also scored twice for England B when they beat a Sheffield XI 5–4 in October 1957, although this match is not included in the England B records compiled by rsssf. Allen travelled with England to the 1958 and 1982 World Cups as the team's official interpreter.
In March 1965 Allen joined Wolverhampton Wanderers as senior coach, working under manager Andy Beattie. Following Beattie's departure, Allen replaced him as manager in September 1965. He was sacked by Wolves in November 1968. He took up the post of manager at Athletic Bilbao on 1 March 1969, leading Bilbao to victory in the Copa del Rey in 1969 and a La Liga runners-up spot in 1969–70. He remained at the club until November 1971. Spells at Sporting Clube de Portugal(1972-73), Walsall F.C.(73-77), West Bromwich Albion (1977), Saudi Arabia National team (1977) and Panathinaikos (1980) followed before a return to his spiritual home - West Bromwich Albion. He succeeded Ron Atkinson - who had just moved to Manchester United. Two of Albion's finest players, Remi Moses and Bryan Robson, soon joined Atkinson at Old Trafford and this had a negative effect on Albion's previously good league fortunes. Albion did well in the cup competitions, reaching the semi finals of both the F.A Cup and the League Cup, although they suffered an early exit from the UEFA Cup. But Allen was unable to put together a good run of form in the First Division and Albion only stayed up after winning their final game of the season. He quit after just one season and was never employed as a manager again.
Ronnie Allen died in June 2001. In 2004 Allen was named as one of West Bromwich Albion's 16 greatest players, in a poll organised as part of the club's 125th anniversary celebrations.