Since we are talking about a style rather than (I'm assuming) any actual content which has been copied, I think you probably don't have a copyright claim. This is because the new publishers have only copied the idea behind the concept but not the actual expression (eg text or images) which you created. Also such things as background shade colour or actual fonts won''t attract copyright on their own. But it's borderline. For instance if you designed a logo or created a variation on a regular typeface, or created a some artwork which forms part of the basic design, say for the masthead, then those sort of individual items could attract copyright, and assuming that they have been re-used in the subsequent editions, then that may be may be something you can use to your advantage.
Even though you did not assign any copyright in such things as logos or repeated artwork it is clear that the client gained implied permission to publish your three editions. However I don't see any reason why it can be assumed that that implicit permission would carry over into subsequent editions which were not commissioned from you, unless the paperwork surrounding the original commission could be interpeted to the contrary. You should also try to recall if there were any discussions/verbal agreements on the subject. If there were, then clearly you and the client may have different memories of what was or was not agreed, but if no such discussions ever occurred, then this strengthens your position because the starting point is that you own the copyright and a written document is required to assign copyright.
On the issue of the copyright notice in the name of the client, assuming that they supplied all the content (text and images etc) then this would be perfectly valid, since these are the principal items which attract copyright.
The other aspect to consider is whether when you pitched for the job or provided an estimate to the client, was this based on the clear understanding that you would get the work on all subsequent editions? So for instance did you submit a lower fee for the initial work based on the assumption that you would be getting regular repeat commissions which would utilise that initial additional work? If this was the case, and you have something in writing promising the future work, then you may have a breach of contract claim. However if you feel that is the case, you may want to speak to a lawyer or Citizens Advice before taking it up with the client as this kind of claim can get quite technical.
And finally, before contacting the client, work out exactly what you want from them. Is it that they cease using any copyright work, such as a logo, which you have created, or do you want them to pay you a lump sum to have the copyright assigned to them? If it's the latter you can raise an invoice for the amount you think is reasonable, and if the client fails to pay, or fails to make a sensible counter offer, you can take the matter further as a money claim
for a relatively modest fee. You can't use this route if you want to make a claim of copyright infringement or a breach of contract claim.