Sometimes yes, sometimes it can wait a day — the difference usually comes down to whether it's actively getting worse or just slow.
Signs it's an emergency
Water backing up and not draining at all, an overflowing drain outside, sewage smells indoors, or more than one drain in the house being affected at once — these usually mean the blockage is further down the system and needs sorting quickly, not left overnight.
Signs it can probably wait
A single sink or bath draining slowly, but still draining, is usually a smaller, localised blockage. Worth booking in rather than ignoring, but not typically something that needs a middle-of-the-night call-out.
What to do while you wait
Avoid pouring more water down an affected drain, and don't use chemical drain cleaners repeatedly — they rarely clear a serious blockage and can make it harder (and less pleasant) for whoever ends up fixing it.
Not sure which one you've got?
Call 07468 868807 and describe what's happening — you'll get a straight answer on whether it needs sorting today or can be booked in, not a sales pitch.