The answer is always no, no matter how friendly you are.
One lawyer cannot represent both parties in a divorce because this could result in a conflict of interest. Divorce is a form of litigation and the English Legal System is adversarial. A lawyer will advise you what is in your best interests, which, given the nature of the dispute, is unlikely to be in your spouse's best interests.
It is not necessary, although it is advisable for you both to have a solicitor. One party could instruct a solicitor and the other could represent themselves. However, the solicitor drawing up the papers will be acting on behalf of one party only and this is worth remembering if you are the unrepresented party.
SEPARATION, DIVORCE AND FINANCIAL BEST INTERESTS
It is also worth remembering that some people don't act in their own financial best interests. Instructing a solicitor does not compel you to take his/her advice, although it does seem a pointless exercise to instruct and then not act upon it. Some people simply wish to know their legal rights and then are quite prepared to act against them. For example, men who have left their wives for other women; men whose wives are the main breadwinners and who are too proud to claim their share; men who don't want their children to be affected financially by the divorce; woman who are scared of their husbands; women who would rather go without than take "his money".