So I brought a new url that goes with my business I used domain forwarding to forward to my main site Would the url still show up in a search engine if the url contains 3 main things that people will type in the search e.g. plumberlondon.com
As far as I know, no it would not because even if you go to it, the page it would crawl is a different domain. I'm not 100% sure on this, but I know dollarhauler.org and dollarhauler.net don't show up when you type in "Dollar Hauler" to Google (and yes, they have been submitted) If you do want to have it show up I think you would need to create a kind of doorway page that links to your mains site, but I'm not a fan of doorways myself. And make sure to watch out for content duplication; Google could penalize your site if it has the same content as another domain.
Google has published guidelines on forwarding URLs. See, Google Information for Webmasters - Question #2: "Once your new site is live, you may wish to place a permanent redirect (using a '301' code in HTTP headers) on your old site to inform visitors and search engines that your site has moved."
domain name - personaltrainerbrentwood.com currently re-directs to optifitpt.co.uk I also have the domain personaltrainerromford.com So If I use similar content on these pages then I will be penalized by google! What if most are the same but some parts are different? e.g.romford and brentwood? will be keeping the old site so will not need a redirect
Google works in strange ways sometimes, hence you might find it takes more time than one would hope for, in order to see results in SERP's