You can, if you have one, but ultimate responsibility will still remain with the company and its directors, as well as the company secretary. The same applies if you delegate these tasks to a third party such as a provider of company secretarial services.
From April 2008, private companies can decide not to have a company secretary. In companies without a company secretary, responsibility for, eg record-keeping and filing at Companies House will fall solely on the directors. Most companies are continuing to have a secretary.