Can my app have a similar name as another business?

The legal rules about brands names and trademarks are specific to each country. However, it's consistant across the EU, and even if the UK left, we could assume they haven't changed those rules yet.

When you register a trademark, you must specify in which fields the trademark will exercise. Then your protection is limited to the specified fields, and somebody else can use the same name in other fields. Because the more fields you pick the more expensive it gets, usually medium companies only pick the fields they need (whereas big companies tend to protect all and every market like Apple https://euipo.europa.eu/eSearch/#details/trademarks/000218990).

For example if I register for "Active Living" in clothes manufacturing, you could totally use "Active Living" for a gym club.

So if your company/app is in a totally different field, chances are that you can safely use the same name.

For more safety, you can check if a trademark has been registered, because if it hasn't you can do whatever you do. To search in the EU there is https://euipo.europa.eu/eSearch/#basic/1+1+1+1/100+100+100+100/reactive social and for the UK it seems it's https://trademarks.ipo.gov.uk/ipo-tmtext and I can't find "reactive social" on any of them so it would mean they haven't registered their name as a trademark, so I think you're 200% safe.

In some cases it can be beneficial. I own ProWriter.co and there a handful of similar sounding brand names (ProWritingAid for example) that people are searching for but end up on our site.

But an exact-match name is a bit tougher for SEO purposes.

I would look for a new domain if I were you.

If they have no registered trademark, you can use this name. But you will struggle with SEO to reach better search positions than they.

Very unlikely you'll have any trouble with that tbh, and it's a different sector, so should not be a problem!