Agar, who was given a part share in the horse by Dame Judi as a 66th birthday present, said: “This is the first horse she has had but she’s never seen it run yet.

“She doesn’t bet but I had a lucky tenner on for her.

“She’s away filming the Cranford Chronicles for the BBC, a period drama, and is staying with friends in Gloucestershire. But unfortunately they’re not racing fans, so she won’t have managed to see it on television.

“But I got a text from her just before the race saying, ’good luck – let me know result’.

“She’ll be more than excited, like I am.”

Key to the result was the rain-softened ground and an instruction from trainer Mark Tompkins to jockey Jimmy Quinn to get the horse settled, which he did as Eradicate cut out the running.

Quinn challenged going into the Dip, drew clear and had enough in reserve as Eradicate fought back in the last 50 yards.

“In his last race at York the seven furlongs was too short for him and he got a bit fresh,” said Tompkins.

“But this time Jimmy settled him well and the ground came good. We’ll keep him to mile-and-a-quarter handicaps at the moment.

“But he’s ground dependent. Either good or good to soft, nothing with firm in it.”

Swiss Franc could be lined up for a crack at the Coventry Stakes or Norfolk Stakes at Royal Ascot after landing the knightfrank.co.uk Maiden Stakes by a length and three-quarters from Wolgan Valley.

Once Ted Durcan set Swiss Franc alight, he left his rival floundering inside the last furlong – despite the colt looking around and showing signs of greenness.

“He was surprisingly green but there’s a lot more improvement in him yet,” said Elsworth.

“We’ll probably look for a conditions race next then possibly think about Royal Ascot – races like the Coventry of the Norfolk – though we’re not sure he’s up to that at the moment.”

Fourth-season Yorkshire trainer Ian McInnes admits to a policy of “wheels will travel” as he looks for suitable races for his string of 30.

And he found the ideal one for his six-year-old gelding Commando Scott, who carried bottom weight in the six-furlong Connaught Square Squirrel Hunt Handicap.

Royston Ffrench brought him with a well-timed run to beat Trafalgar Bay by a length, giving McInnes his first victory at Newmarket.

“We have been waiting for this rain. I’ve been ringing Michael Prosser (Newmarket clerk of the course) constantly for 48 hours asking if he’s had rain,” said McInnes, who is based near Beverley.

“It came just in time and Royston’s given him a cracking ride.

“We don’t know where we’ll go next, but the horse must have a bit of cut, not necessarily soft.

“That’s our 15th winner of the season.”

Jimmy Fortune bided his time on Transcend in the seven-furlong Capital Spreads Maiden Stakes before unleashing the colt to collar long-time leader Esteem Machine inside the last furlong to win by two lengths.

Winning trainer John Gosden said: “The ground was a bit quick for him last week but he ran well in what was a hot maiden.

“The ground was the difference.”

Gosden refused to be drawn on a target for Transcend but said: “He’ll go where the rain is.”

The EBF Fillies’ Handicap Stakes over six furlongs went to Goodbye Cash, who belied her name to land a gamble.

The David Evans-trained filly was backed from 9-1 to 7-2 favourite and held the challenge of the also-gambled Ken’s Girl by half a length.

Evans claimed he had not backed the filly because she was “plenty high enough in the handicap”, but felt she would handle the track, distance and ground better than she had done at Chester last time.

“The rain does it for her,” he said.

Successful jockey Stephen Donohoe was hit with a one-day suspension (June 7) for careless riding.

They All Laughed was booted to a popular verdict in the Birdwells Ladies Handicap, while Tompkins doubled up in the concluding Countryside Raceday Handicap with Oscarshall (10-1).