Thanks for the question! The answer is a bit complex, so I'll break it down by topic.
First, Moz does recommend here that people use top-level domains (such as .uk) and not second-level domains (such as co.uk). This is what you're now doing.
Second, you've done everything correctly as far as 301 redirects and GWT notification of domain change. (One possible note: If your target audience is primarily people in the UK, then you should also state that designation in GWT in Search Traffic > International Targeting.) If you're not doing this already, I'd also select a web host that will give you an IP address that is located in the UK.
Now, it's been only ten days? I'd humbly suggest that it's too soon to make any judgments. Whenever a major change is done to a website -- such as as moving a website to a new domain -- it takes time for Google to "catch up." Until that time, things will be a little "wonky" (to use UK slang). I'd give it a month -- possibly a little longer.
You're correct that the length of time that a domain has actively existed is a ranking factor. But as long as you've done everything correctly to "tell" Google that the domain has moved to a new domain, then that length of time should "carry over."
Lastly, I'd do whatever you can to get high-quality backlinks to the new domain that are 100% earned -- think of how to get natural publicity on any major, authoritive sites that are read by your target audience.
If you're still having problems after a month or so, I'd post here again -- I'm sure the Moz community will be happy to help again. Good luck!