I buy & sell shares as part of a work scheme. The company which I use to manage my share portfolio is Computershare which I find very good. My company pays for the use of Computershare as part of the share scheme so I'm not sure how much it costs to manage a portfolio.
I would recommend contacting them. Alternatively I would also suggest looking at the share certificate which would have been attained as part of the inheritance as the company managing the share portfolio would be on it. You could contact them for advice. Different companies/share portfolios have different rules so it difficult to advise on selling. I for example to achieve maximum tax efficiency need to keep my shares for a minimum of 3 years before selling. If I sell before it's subject to paye which is a significant chunk. Selling shares before or after the 3 years is subject to prsi and USC. Regarding timing, if I advise Computershare to sell today I receive the money within a week but again you would need to confirm this is the same.