[1] Webb moved to a senior lectureship in medicine at the University of Edinburgh in 1990, where he directed its newly established Clinical Research Centre.

[3] He also participated in raising awareness about poor medical undergraduate prescribing skills[4][5] and in 2009 he provided evidence to the United Kingdom select committee on patient safety regarding prescription errors,[6] of which an excerpt is shown below: It is widely recognised that newly qualified doctors are at the sharp end of prescribing, and that this work is largely unsupervised.

Although junior doctors are protected from undertaking many high-risk practical procedures, they are able to prescribe powerful medicines from their first day of clinical work.

[8][9][10] Webb's scientific research focuses on novel treatments for hypertension and cardiovascular risk, particularly with regards to blood vessel structure and function.

He was appointed Commander of the Order of the British Empire (CBE) in the 2020 Birthday Honours for services to clinical pharmacology, research and education.