First, to reiterate:
Please use example.com in posts in this forum
Eventually people get tired and stop saying "please". Or, conversely, people figure out why they have to put gratuitous spaces into lines like
The url for subdomain is http ://m.domain.co.uk which redirects from http ://www.domain.co.uk/m
Does it redirect-- the user's address bar changes-- or does the user type in "m.example.co/" and get served content that lives at "www.example.co/m/" ? Or the other way around? Or neither?
You say "the above code". But you've got two separate rules and it's important to understand they have nothing to do with each other. In particular, the Condition only goes with the first Rule, whether that rule executes or not.
Rule 1 is a redirect with accompanying condition:
RewriteCond %{HTTP_HOST}%{REQUEST_URI} ^(www\.)?example.co.uk/webstores/ecommerce/(.*)
RewriteRule (.*) http:/ /m.example.co.uk/%1 [R=301,L]
Yes, OK, so sometimes even "example.co" isn't enough. Is this rule supposed to be about the host or about the body or the URI? It's generally safer to deal with one thing at a time, especially when you're not sure what you are doing. If the Rule requires you to look at the host, make that a Condition by itself. And then dump the REQUEST_URI part and shift it to the body of the Rule. You don't need to say the same thing twice. Here what you've really got is a redirect from
/webstores/ecommerce/.*
to
http:/ /m.example.co.uk/www.
-- the "www." is the first capture in the Condition-- which is clearly gibberish, so you must have left something out. Although both the Rule and the Condition capture the request, neither capture shows up in the target.
Rule 2 is a Rewrite without conditions:
RewriteRule ^(\d+)/([^/]+)/?$ /shopping-cart/index.php?uiid=$1&title=$2 [L]
This rule takes input in the form "www.example.com/one-or-more-numbers/more-stuff with optional final slash" and serves content from www.example.com/index.php?uiid={the numbers from the request}&title={the rest of the request}. Is that what it's meant to do? Is this the part that isn't executing?
While you're working on it, do something about the optional final slash. You've created a duplicate URI, which is never good. It would be fine in a redirect, because the user ends up in a different place anyway. But never never in a rewrite.