Well, if you use Firefox, you can get the history listed and simply zap all references to Mumsnet. Or, simply open a new window and then under 'Tools' choose to "Start Private Browsing".
Desription for Firefox browsing:
In a private browsing session, Firefox won't keep any browser history, search history, download history, web form history, cookies, or temporary internet files. However, files you download and bookmarks you make will be kept.
On Google Chrome - on a thread link, right-click, and choose 'Open link in incognito window' - you will now see an empty window, with a dark border and the outline of some guy wearing a hat, like some 'spy'
Browsing in incognito mode only keeps Google Chrome from storing information about the websites you've visited. The websites you visit may still have records of your visit. Any files saved to your computer will still remain on your computer.
I feel sure Microsoft's Internet Explorer browser also has similar "private" mode.
On one hand the OP should not need to feel her activity on MN could be monitored, and these features have been added for "hiding" browsing activity - perhaps from a "shame" point of view, but for someone (not the OP) needing to be able to research where she might go - eg a women's refuge - it could provide the opportunity without risk of the history giving away those searches and websites visited). Do please, if you see someone in need, mention the possibility of searching 'incognito'. However, please remember that 'favourites' (aka 'bookmarks') are not guaranteed to be safe from viewing hours or day later.