2018: two-year-old season

On his racecourse debut Oxted started at odds of 33/1 for a maiden race over six furlongs on soft ground at Doncaster Racecourse on 10 November. Ridden by Liam Keniry he kept on well in the last quarter mile and finished fifth of the fourteen runners, beaten nine lengths by the winner Dazzling Dan.^[6]

2019: three-year-old season

Oxted began his second campaign on 28 April at Salisbury Racecourse in a novice race (for horse with no more than two previous wins) over seven furlongs in which he was ridden by David Probert. Starting a 25/1 outsider he recorded his first success as he disputed the lead from the start and won "readily" by two and a quarter lengths from The Night Watch.^[7] When he was stepped up in class for the Listed Carnarvon Stakes at Newbury Racecourse three weeks later he led for most of the way before being overtaken in the final strides and beaten half a length by Khadeem. He then ran sixth behind Waldpfad in the Group 3 Hackwood Stakes at Newbury in July and finished a distant last of four behind Tabdeed in a minor race at Doncaster Racecourse on 3 August. Two weeks later he was assigned a weight of 128 pounds in six furlong handicap race at Newmarket Racecourse and ran second to his old rival Dazzling Dan beaten half a length after finishing strongly.

At Doncaster racecourse on 14 September Oxted started at odds of 14/1 in a twenty-two runner field for the Portland Handicap over five and a half furlongs on good to firm ground. He was assigned a weight of 133 pounds but carried three pounds less as he was ridden by the apprentice jockey Cieren Fallon. He raced just behind the leaders down the centre of the course, went to the front inside the final furlong and won by half a length from the six-year-old gelding A Momentofmadness (winner of the race in 2018).^[8] He was the first horse of his age to win the race since 2000. After the race Roger Teal said "He'd started to shine in his work so we were pretty hopeful, but I started panicking when I looked at the stats for three-year-olds. It was an amazing day in the end. He's still a baby and only a frame at the moment. He's worth giving a chance to and I think he could be seriously nice next year."^[9]

2020: four-year-old season

The flat racing season in Britain was disrupted by the COVID-19 pandemic and the Group 3 Abernant Stakes, which saw Oxted make his first appearance of the year, was run on 5 June behind closed doors at Newmarket. The gelding started 7/2 second favourite behind the Prix Maurice de Gheest winner Brando in a seven-runner field which also included Emaraaty Ana (Gimcrack Stakes), Breathtaking Look (Sceptre Stakes), Mr Lupton (Greenlands Stakes) and Keystroke (winner of the race in 2019). Ridden by Fallon (still an apprentice but unable to claim a weight allowance in a Group race), Oxted went to the front approaching the last quarter mile, accelerated into a clear lead, and held on in the closing stages to win by a length from Breathtaking Look.^[10] Teal commented "It has been a stop-start campaign and I had him primed to run in this in April. Thankfully we eased off with him and when we got the date for this we knew what was happening so we stoked him up a bit and God bless him he has done it well. He popped out and travelled lovely. I saw him powering up the hill. Cieren said he was just having a bit of a look around, but he did it nicely".^[11]

On 11 July Oxted was stepped up to the highest class to contest the Group 1 July Cup over six furlongs at Newmarket in which he was ridden by Fallon and started at odds of 12/1 in a twelve-runner field. Golden Horde started favourite while the other contenders included Hello Youmzain, Brando, Khadeem, Sceptical (Woodlands Stakes), Threat (Gimcrack Stakes), Equilateral (Scarbrough Stakes), Southern Hills (Windsor Castle Stakes), Namos (Silberne Peitsche) and Sir Dancealot (Lennox Stakes). Oxted tracked the leaders as Golden Horde set the pace before gaining the advantage in the last quarter mile and keeping on well to win by one a quarter lengths from Sceptical with the favourite a neck away in third.^[12] After the race Fallon said "He's very fast and versatile, he's won over five and a half and seven, he goes on soft and quick. It shows what a good horse he is and I was just a passenger on a very good horse".^[13] Shortly after the race the gelding underwent surgery to remove an ulcer from his throat.^[14]

Oxted returned to the track for the British Champions Sprint Stakes over six furlongs on soft ground at Ascot Racecourse on 17 October and started the 9/1 fifth choice in a sixteen-runner field. He was among the leaders from the start and gained the advantage a furlong out but was overtaken in the closing stages and finished fifth in a blanket finish behind Glen Shiel, Brando, One Master and Art Power.^[15]

In the 2020 World's Best Racehorse Rankings, Oxted was rated on 120, making him the equal 40th best racehorse in the world.^[16]

2021: five-year-old season