Not a great deal to add to what has been said already but I will include my tuppence worth (we barristers clearly charge far less than those useless £200 per hour solicitors) anyway.
Technically, any covenant that acts as a restraint on trade is void. That is to say that it would be unlawful to attempt to remove the right of a former employee to gain a living from their chosen profession. However, there is a "but" - a big
but - and this relates to whether the covenant is in place purely to protect a legitimate business interest and whether it is
reasonable for the purposes of such protection. If that can be shown - and it is the responsibility of the employer to present an appropriate level of evidence - a court is likely to enforce the clause.
The important word in your context is
reasonable. If the clause is not considered
reasonable then it would be void. In order to be
reasonable the clause must set out geographical-, duration- and activity-based restrictions - and these must be justifiable in terms of protecting the employer’s business.
The clause you have really is shockingly worded. For a start, what exactly is the difference between “working with” and “working in conjunction with”!? However, it does specify the duration element (although 360 days is frankly ludicrous in relation to the nature of the business) but nothing else. Leaving the geographical and activity elements completely open-ended would not be considered
reasonable and would, therefore, render the clause void. So you have nothing about which to concern yourself.
TLDR version – shock horror Mags is spot on (almost)!
[edit] oh, and the fact that you are a contractor would not change the position either way.