For actor Ilan Goodman there was a tad more than usual to consider while preparing for his role in the UK premiere of Red Light Winter at the Theatre Royal in Bath.

On top of the quick-fire dialogue spoken by his character Matt, a lovelorn writer on the verge of a nervous breakdown; and aside from the rehearsal-room tension of getting naked for the raw and tender sex scenes with his co-star Sally Tatum, there was the slight distraction of knowing that his famous father Henry was rehearsing in the same building for a different play, Michael Frayn's Copenhagen.

"I sort of don't mind it," says Ilan on the last day of rehearsals, though he is not talking about the proximity of his father, but the stress of getting his kit off in front of strangers. "If I'm brave enough to do it I think that's really cool. But at the same time, all one's insecurities flare up. I have to go back in soon and get naked again." Although it is the last day, there is still important work to be done, particularly the sex scene which is proving to be one of the most challenging in the 30-year-old actor's short but promising career. It is not something he has had to do before. At least certainly not in a recent revival of Arnold Wesker's Chicken Soup With Barley at the Royal Court, nor in Six Degrees of Separation at the Old Vic, nor the other plays in which he has appeared since he graduated from RADA in 2007.

Acting dynasties are not that rare. But watching your father scoop awards and acclaim - the landmark Shylock at the National, the memorable Richard III for the RSC or the lawyer Billy Flynn in Chicago, to name but three - well, it could cast a shadow over a son with ambitions to go on the stage.

"That hasn't really ever haunted me," says Ilan breezily. "There are moments when people say strange things. One chap recently told me that I will never have made it as an actor until I had done better than my father. And I said: 'Well, I'm f***ed if I use that criterion. And I don't, and it wouldn't be sensible for me to. I won't feel burdened by it until the day we act together. Then it will become a kind of comparison."

One chap told me I willnever make it as an actor until I do better than my father

Judging by the reviews Goodman the younger has received for Red Light Winter, he stands every chance of not being upstaged by his dad if they do act together. And now that the trajectories of their careers have landed them in the same rehearsal studios, that day must surely come soon. Do they talk about which play it would be?

"There are lots of plays about Jewish families," Ilan muses. "Or perhaps it should be one that is not so literal. But I think it would make sense if there is a father-son relationship. One day it'll happen."

Before RADA, Ilan was at Oxford reading psychology and philosophy. The former discipline is certainly a good grounding for an acting career. The latter might come in useful for those periods when actors fall out of work, a prospect that Henry made sure his son was always aware of. The way the son describes it, it sounds like the father was less than madly enthusiastic about his son following in his footsteps.

"I'd call it judicious wariness," says Ilan. "He tried to instil an understanding of the likelihood of unemployment. He was of course a terrible role model in that respect. He is almost never out of work."

Like the father, the son started acting very early, although the circumstances and the reasons were very different. Henry had a tough East End childhood, made tougher by a father who was schizophrenic and beat his mother. Acting was an escape. Ilan's formative experiences were entirely positive.

"When I was really young, I think about eight or nine, we were living in Stratford-upon-Avon and I had a walk-on part as a street urchin in The Beggar's Opera at the RSC [where his father was part of the ensemble]."

It is hard to tell, says Ilan, if he has developed an acting style similar to that of his father. If he has, it is via a different route. Henry immerses himself in a role through, as Ilan puts it, "huge amounts of preparation", which involves a lot of reading and thinking. "He gets into a role imaginatively," says Ilan. "It's definitively not 'method'," he adds, referring to the process that can involve inhabiting a role off-stage. "I think I do more of my discovery in rehearsal."

There are, no doubt, advantages in being an actor with a famous actor father. But there is a price too. "We see each other's stuff and offer brutally honest critical feedback," says Ilan. "You can do that as a family member. It comes from the point of view of compassion and constructive criticism. I was probably harsher when I was younger. I remember when he was in Chicago telling him that he wasn't anywhere near cool enough."

The advice clearly worked. One critic described Henry as being so cool in that role, you could ski down him. And now, with lunch over, the time has come for Ilan to play it pretty cool too. "If you'll excuse me. I have to go back now. I think I have to take my kit off again."

'Red Light Winter' by Adam Rapp is at the Ustinov Studio, Theatre Royal Bath until March 31. Tel: 01225 448 844, www.theatreroyal.org.uk/ustinov