Wow, we think about risk really differently. My thoughts are:
Your business income isn't increasing, not even with inflation(?). This would concern me, assuming you are doing a similar amount of work. Is the business sustainable, what are the competing technologies, how secure is the business/industry you contract for. Cash, even for 5 years, won't save you from this risk. Is your business going to age out (think typewriter maintenance) or is there something you can do to pivot to a growth area? You could still keep working for yourself but look for other contracts. The transition from contractor/owner to employee is often not smooth, which could be weighing against you in applications.
However, you don't have to stay in the same line of work. If you lost your contract, what do you think the likelihood is that you could find ANY job? Would this be acceptable to you?
If you aren't interviewing well, try
Ask a Manager, watch out for things that are US-centric, but it's a great resource.
Based on your situation, I agree that you should hold more cash than average. I still think you are holding too much. The question I'd be looking to answer is: if the market is down when the income stops, how long do I want to be able to spend cash while I'm waiting for a recovery. For me, that feels like a year, max. You may also want to think about your ability to spend some non-company cash first to get the company cash out in the next tax year.
Do something with the cash, when you factor in inflation, you aren't getting a whole lot back, especially as you run out of the best accounts to put it into. Any money that you don't need to spend within 2 years should be doing something useful IMO: I'd send it to the S&S ISA. If that makes you nervous then drop your monthly surplus into the S&S ISA as you go.
Have you looked into the risk of P2P lending? The risk / reward ratio doesn't do it for me unless there is something sweetening it for me. I'm not convinced that it is guaranteed to stand up in the event of a big market crash - and that's effectively why you are holding cash: to allow you to wait for your shares to recover.
There might be space to trim your spending if you are interested? Is the £1.6k your 'bare bones' budget rather than your current spending? For how many people and where? Consider going through your current spending: highlight everything discretionary that you wouldn't spend if there was no income coming in. Look at the list and really think about whether you'd feel more relaxed about your contract if you were saving a little more.