It basically had 0 impact as the earliest jet airliner, the de Havilland Comet, emerged from a contemporary research and development pipeline that was seeing results and developing aircraft at the same time as the 262's development.

The de Havilland company, most known probably for the Mosquito strike fighter, had been involved both in pre war commercial aviation, and in the development of some of the first jet engines and flying aircraft. For instance the first prototype of the eventual Vampire and Sea Vampire flew in mid 1943 only a few months after the Gloster Meteor, and its Swallow prototype in mid 1946 with both DH aircraft powered by the Goblin turbojet engine developed in house that would also power some other early jets including an early Saab design.

However a British Commission lead by the Lord Brabazon had been set up in 1942 to examine the needs of British civil aviation following the war, both internationally, domestically, and in connecting the widespread Empire and Commonwealths. In the end 5 different need for various distances, and carrying capacities for a robust system were decided on. And most notably #4 was a jet airliner that could outpace and outdistance most other medium and large commercial aircraft then in service, while another was for a very large turboprop transatlantic aircraft.

On the committee then was one Geoffrey de Havilland who pushed for and one the contract for the jet airliner to be powered by his new more power Ghost engine. This same engine would power the Venom and Sea Venom for the RAF, FAA, and French Navy, and the Saab 29 early Swedish jet fighter.

From that the program to develop an aircraft that would make British aviation the envy of the world was born(and head off further dominance of the sales market by American companies like Boeing). Soo in 1949 the de Havilland Comet was first shown to the public and Farmbourough, and first flew in 1952, with deliveries and commercial service beginning during the next 12 months. It was an instant sensation and notables and the public flocked to see it, including even some Royals such as The Queen Mother!

But incidents began to pile up for the new jet which would soon spoil its reputation. First it was simply runway overshoots and space issues on the runways attributed to pilot error in a bleeding edge plane. But things didn't get better, in 12 months from May 1953 to April 1954, 3 Comets suffered fatal accidents including 2 in 1954(Jan and April) breaking up in midair killing all aboard in each of the 3. Initially many causes up to even sabotage were suspected, but after testing it was found that the pressurization cycle for the aircraft fatigued the air frame to the point of failure due to repeated stress from its flights, made worse by designs featuring things like square window.

And after repeated groundings after each accident, and eroded public confidence, the whole project was doomed despite design revisions to correct the errors. In all less than 100 Comets would ever be built or fly. Meanwhile the same summer of 1954 while the Comet's errors were being examined Boeing would test fly the first of what would become more than 800 707's.

For a little deeper dive into the aircraft, but not overwhelming you may enjoy this article from the Smithsonian: https://www.smithsonianmag.com/history/comets-tale-63573615/

They also have a bit about the failed transatlantic aircraft called for the aptly named Bristol Brabazon: https://www.airspacemag.com/history-of-flight/cancelled-design-by-committee-118026858/

In general German and British early jets and jet engines developed independent of each other, both saw functional prototypes early in the war, and operational models by the end of the war. While the US programs got a big boost from British cooperation, one of the first US jets, the Lockheed P-80 was actually originally supposed to be powered by the Goblin engine in fact but production delays ended that. While General Hap Arnold attended a GLoster test flight in 1941 and managed to secure plans and engine examples from which General Electric began producing versions and then derivatives of to begin their long association with jet engines. The resulting Bell P-59 aircraft wasn't as revolutionary as had been hoped, especially with reports of the Me-262 coming out, but it was still a start too.