The others are Richie Ramsay () and Graeme Storm (), who was tipped up by our golf expert Dave John pre-tournament at 110/1.
Odds correct at 1745 BST on 30/09/17.
Poulter may well be in contention for a first victory in five years but was furious when finding water with his tee shot on the par-three fifth after being distracted by spectators taking pictures on their phones.
"What are we doing?" an irate Poulter said. "We've allowed them all to take pictures and videos and tell them to put them on silent, and it doesn't work does it?
"You get distracted on the wrong hole at the wrong time and it's extremely penal and it's really f****** annoying."
Asked if mobile phones should be banned - as they are at Augusta National for the Masters - Poulter added: "No, I just think people need to educate themselves and understand it's an issue for us and them. They don't realise they distract us as much as they do. Ninety nine per cent of them are on silent and unfortunately there's a couple which are not. You're not expecting it because you think they've got it on silent.
"I'm angry and am going to continue to be angry until I wake up tomorrow morning. Throwing shots away for no reason is really annoying."
McIlroy was in a far better mood, saying: "You get yourself into contention and you start to think about things and it would be nice to get a win. The crowds have been fantastic. The last couple of tournaments I've been off pretty early on the weekends and had 50 people following me, where there's thousands out there so it's nice to get into that sort of environment again."
Storm was equally happy to see McIlroy's name in the frame, having beaten the Northern Irishman in a play-off for the South African Open in January. He said: "I saw his name go on the leaderboard and I was thinking this could be a bit of an omen, something which could be great for me again. I'm disappointed I'm not leading the tournament to be perfectly honest. I missed short putts on 12, 13 and 14 and should have been sitting pretty on the top of the leaderboard, but we're in with a shout and that's all I can do."
Tyrrell Hatton roared into a three-shot lead and spearheaded an impressive English challenge at the top of the leaderboard on day two of the British Masters supported by Sky Sports.
Hatton defied the wet and miserable early conditions to add a composed 65 to his opening 63 to hit the front on 12 under par, and he is one of a remarkable seven English players in the top 10 at the halfway stage at Close House.
Tournament host Lee Westwood and fellow veteran Ian Poulter are among the chasing pack in a share of second while Rory McIlroy recovered from a poor start to make the cut with plenty to spare, but Masters champion Sergio Garcia played one shot too many to avoid a weekend off.
David John's 110/1 pre-tournament pick Graeme Storm is four shots behind Hatton and is now as short as to lift the trophy.Hatton was out early in persistent rain and chilly conditions, but he made light of the unpleasant weather and got off to a flying start from the 10th with three birdies over his first four holes.
The overnight joint-leader extended his lead further with another gain at the 17th as he covered the back-nine in 31, and he picked up another shot at the fourth before making his only mistake of the day three holes later.
But it could have been a different story for the four-time major winner if a spectator had not found his ball inside the five-minute time limit after a wild drive on the 17th, his eighth hole of the day.
McIlroy produced a superb recovery from thick rough to the elevated green and went on to make three birdies on the front nine in his penultimate tournament of an injury-plagued season, which the former world number one will bring to an early end after next week's Alfred Dunhill Links Championship.
"It's not a bad way to feel," the 28-year-old said. "You're not really looking ahead at anything, you're just concentrating on the round out there and not thinking about anything else.
"I feel like I'm not under any pressure to perform at all, I'm not putting myself under any pressure. That's probably the reason I've went out there and shot a decent score.
"I think if you asked 75 per cent of the guys out here they would say it would be nice to have some sort of an off-season.
"I'm just giving myself an off-season this year and looking forward to improving my health, improving my game and becoming a better player in 2018."
And it's Hatton who is to double his European Tour tally almost exactly a year on from his breakthrough.
Storm, tipped at a three-figure price by our golf expert David John prior to the event, is into to provide local fans with something to cheer, having been born in Hartlepool.
Slattery, who made worldwide news when he watched his wife give birth to their second child via FaceTime while he competed in Switzerland, carded five birdies in a flawless 65 compiled alongside 16-year-old amateur Robin Tiger Williams.
Williams, who was born in the year that Tiger Woods completed the 'Tiger Slam' of holding all four major titles at once, carded a highly respectable 71 and said: "It was so fun and enjoyable.
"I had trouble getting to sleep on Wednesday night and I was definitely nervous on the first tee, but as I got into the round I settled down and handled it very well."
Tournament host Lee Westwood, Martin Kaymer, Matt Fitzpatrick, Graeme McDowell and Ian Poulter all shot 66, but Masters champion Sergio Garcia had to settle for a level-par 70. Defending champion Alex Noren finished one over.