In the States, we would ask, “can I help,” if we saw someone in actual need of help (e.g., struggling to reach something on a high shelf, trying to get the top off of a jar, unhooking a bra, etc…). Here in London, the phrase means, “next,” and not much more.
So when the person behind the counter at the grocery store ask you, “can I help,” just move forward and give them your items rather than telling them about your rash that won’t go away or asking if you can borrow five quid from them for your groceries.