The 19-year-old centre, a graduate of the Exiles' academy, has scored four tries in his first three appearances.
Two of those came on his Premiership debut against Wasps in front of a crowd of more than 42,000 at Twickenham.
"Scoring at Twickenham, it's something I've dreamed about since I started playing at the age of six," he said.
But, the Reading-born inside centre is keeping his feet firmly on the ground as he targets both a continued run in Tom Coventry's side and a first Premiership win of the season for Irish.
"We've been unlucky with injuries in the centre and I've been given a shot," he told BBC Sport.
"I know those players are coming back and they're fantastic, but I'd love to keep the number 12 shirt and I hope I do.
"For me, it's about getting this experience and trying to be the best player that I can."
Williams, who has already represented England at under-17 and under-18 level, is now hoping to break through into the under-20 squad.
His brace against Wasps caught the national for the first time, but he still found fault in his own performance.
"I don't think I carried the ball as much as I have in previous games," Williams said.
"I made a lot of tackles as we spent a lot of time without the ball. It was a fantastic occasion with lots of friends of family, but it was a shame about the result."

The Wild Dolphins project was organised by Wild in Art along with the Archie Foundation at the Royal Aberdeen Children's Hospital, and Whale and Dolphin Conservation (WDC).
For the last 10 weeks they have been the most photographed and talked about attractions in the city.
They were in parks, shopping centres, the beach and museums.
The models will now be auctioned.
The auction will be held at Aberdeen's Music Hall on Wednesday 10 September from 19:00.
Proceeds will be split between Archie and WDC.

The 28-year-old male officer suffered serious burns and is in an induced coma, prosecutor Eric Lallement said.
His female partner was also badly burned on her hands and face.
The attack in the town of Viry-Chatillon was a "murder attempt", a police union official told RTL radio.
The officer with the most serious injuries was "between life and death", said Claude Carillo from the Alliance 91 union.
The officers were on patrol near a housing estate. Robbers have been known to target motorists at a traffic junction in the area.
A group of about 15 people were involved in the attack and surrounded the patrol car, the AFP news agency reports.
Two other officers who arrived as back-up were also injured.
Prime Minister Manuel Valls said those responsible would be "relentlessly pursued and brought to justice".

26 July 2016 Last updated at 11:23 BST
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CCTV images of Francesca Galelli and Molly Curtis, both 13, were circulated by Cambridgeshire Police.
But the force issued a correction after it emerged the girls were not responsible for the theft from a branch of Superdrug in Ely.
Sgt Phil Priestley said police had made an "innocent mistake".
He said: "We always want to be clear and transparent if we get things wrong, and we definitely want to ensure that people know that Francesca and Molly are good people from lovely families, and this wasn't their fault".
Cambridgeshire Police have revised district CCTV policies to prevent such mistakes from happening in future.
Johnny Williams knows he has a fight on his hands to keep hold of the number 12 jersey at London Irish, despite a whirlwind start to his senior career.
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