Short answer: yes, always. It's one of those things people mean to get round to and then never do. But it's worth doing in the first week, before you've even unpacked properly.
You don't know who has a key
By the time you pick up your keys on completion day, a surprising number of people have had access to them. The previous owners, obviously. But also family members who had a spare. Cleaners. Neighbours. Workmen who came in while the house was being sold. And the estate agent, who typically holds a set of keys for weeks or months during the viewing period.
Think about that last one for a moment. A set of your house keys sat in an estate agent's office, going through multiple hands, often with a key tag that has the address on it. Who's copied them? Genuinely, nobody knows.
Changing your locks means none of that matters anymore. You start fresh with keys you control.
Rekeying vs replacing
There are two options. Rekeying means a locksmith adjusts the existing lock so the old keys no longer work and a new key is cut. It's cheaper because you're keeping the same hardware.
Replacing the lock means fitting a new cylinder or new lockset entirely. It costs a bit more but it's the better choice if the existing locks are old, low quality, or if you want to upgrade at the same time.
My advice: if the locks are more than a few years old, or if they're cheap-looking cylinders, replace them. The price difference isn't large and you'll have something worth having.
Moving house is the ideal time to upgrade
If your new home has a UPVC or composite front door, check what cylinder is fitted. Standard euro cylinders are vulnerable to a technique called lock snapping, which is how a large proportion of UK burglaries happen. Moving in is the perfect time to swap it out for an anti-snap cylinder before you're settled in and it slips off the to-do list.
A TS007 3-star rated cylinder costs very little more than a standard one and takes the same amount of time to fit.
What I do across the Wirral
Moving-house lock changes are one of the most common jobs I get called out for. I'll come and look at what's fitted, tell you honestly what's worth keeping and what should be replaced, and fit new locks on the spot. Most people want it sorted on the day they move in, which I understand. Call ahead and I'll make sure I'm available.