There is actually little to no evidence of a mass movement of people from Continental Europe to Britain or Ireland during the time period a 'Celtic' people (a concept that is itself somewhat suspect) are documented to have lived on Mainland Europe (that is to say the mid to late Iron Age).

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That said, while we don't have urban centres in Ireland arguably until the Viking period (around the 8th/9th centuries AD), there are plenty of examples of thee results of collective labour dating back to the Neolithic. A good example would Newgrange passage tomb, which is a relatively sophisticated piece of engineering. It consists of a cruciform passageway of large upright stones with a strong roof made by corbelling (a way of building out over open space by overlapping stones) all covered by a cairn (mound) of stones. What is most interesting is the 'roof box'; an opening over the entrance which, on the shortest day of the year, allows the rising sun to shine all the way down the main passage (a distance of 19 metres). The tomb would have required a lot of work both to build and to work out the astrological alignment needed to angle the entrance, so we can safely say that society was organised in such a way that a lot of labour could be directed towards the creation of what was probably a central religious or ritual place for a large area. Staying in the Neolithic and moving to Britain, Stonehenge in Britain is another example of a large organisational effort: 42 of the stones were quarried in Wales, over 180 miles from the location of the monument. While that does it for the existence of 'Public works' from very early on whether these things indicate the existence of what we could reasonably call a state is another question entirely, so we need to move forward a bit for the urbanism question

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Into the late Bronze Age and the Iron Age, Britain does see the development of large enclosed settlements known as hillforts which, particularly in Southern Britain, become what you might call central places but whether they're actually 'Urban' in a true sense is unclear. Usually an urban centre would have buildings with a public function (religious, administrative etc) but these hillforts could equally be the fortified dwelling of the local elite as a statement of power and control over the local landscape; control because they're normally located in a high position that can overlook the surrounding territory, and power because they are surrounded by massive complexes of earthworks (see Maiden castle for a good example), which would have taken a massive amount of labour to construct. Much like the Neolithic passage tombs, being able to direct a large amount of labour could have been a way to reinforce the hierarchy but also to create a group cohesion; Iron Age British settlements were small, spread out affairs, bringing everyone together to dig a ditch might have solidified relationships between people who simply weren't all together in one place very often and simultaneously remind them who was boss!

That being said, particularly in the South of Britain it seems that these hillforts were starting to become something that we might understand as urban as we move toward the Roman conquest in AD 43; they enclosed a large number of densely packed buildings, the landscape surrounding them is often empty of other settlements and they seem to have been the storage area for large quantities of food gathered from the surrounding areas and presumably controlled the food supply within their 'catchment'. On the other hand, it seems that the British Iron Age hillforts distinctly lack the craft specialisation that is often used as a defining feature of an urban centre at this time on the continent, that is to say it doesn't look like these hillforts were the location of production of specialist or high quality items. As well as that, they lack the administrative/public spaces one would expect from an urban centre that I mentioned earlier

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At the end of the day, whether the British hillfort tradition is a sign of a move toward urbanism is a matter of definition, and is probably coloured by the fact that our point of comparison are the settlement types of the Greeks and Romans of the same period. Should we expect all human societies to construct their settlements in a way that conforms to a specific hierarchy? Should we even expect an evolution of society from less centralised to more centralised?

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A great recent paper on the concept of Urbanism in Late IA britain from which I got most of the info for the second part of this comment is "Are the developed Hillforts of Southern Britain urban?" by Niall Sharples in the book Paths to complexity: Centralisation and urbanisation in Iron Age Europe edited by Manuel Fernandez-Gotz, Holger Wendling and Katja Winger

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Edit: run-on sentence made legible and source added