A comedy about a liver transplant is not an easy thing to deliver. But Delivered is the title of this new play – in Cambridge’s newest theatre – The Town and Gown.

The glitzy pub on several floors – with a theatre on the top - is in Market Passage, in the centre of the city, in a building that once housed the Arts Cinema. It’s a place that feels full of style and a must for performance.

In this slickly played two-hander, Jessica Melia plays Tabitha, a young woman from Birmingham who has had a liver transplant and has set out on a mission to meet the family of the donor.

Her trail leads her to the home of another young woman called Kate.

She turns up in Glasgow on the doorstep of Kate’s husband, Tim (played adroitly by Adam Boyle) who she finds just doesn’t want to know. He doesn’t want contact. It’s Friday night, it’s tea-time and he is cooking fish fingers for his seven-year-old daughter.

But something makes Tim – possibly to get her to leave – give Tabitha his phone number. A feisty relationship ensues. There is a lot of humour here.

The audience spent a lot of time chuckling. But this is no Beatrice and Benedict. It’s no Harry met Sally. Writer and director Lisa MacGregor has avoided any schmaltz.

This is not a sentimental show. Our main characters are flawed. Tabitha is fixated, Tim is conflicted, Kate, we find, had her own problems.

Tabitha persists in trying to establish a relationship with Tim, largely against his will.

In a play called Delivered she brings to him a pile of letters she wrote after her surgery thinking that no one would read them – but now she desperately wants him to.

This is a thought-provoking and memorable play. It may be important for the person receiving an organ transplant to know the person who gave it – but how much does it help the family of the donor?

This debut play from Lisa MacGregor is sharply written and tightly directed. Does it deliver – yes, I think it does.

Delivered is at The Town and Gown, Cambridge until Thursday, November 17 then at Birmingham Old Joint Stock from November 19-21.

The play is supporting University Hospitals Birmingham Charity.