Who is responsible?
Consider the following:
You are only responsible for the work that can reasonably be expected of you to finish.
As you said yourself, you are not in a manager position. Your job is to get as much work done during your normal working hours. It's advisable to work as efficient as you can and this has very little to do with how efficient your coworkers do their job.
If the customer is unhappy they should be complaining to your manager (or whoever higher up is responsible for "selling" the product and the support for it). Then when your manager comes to you, you have to be able to honestly say: "I have done everything that I could.". It is your managers responsibility to either reduce the work load on your team, or find other solutions to keep the customers happy, not yours.
To support your claim, you also want to have some tracking. At our job we use jira to track issues along with coupled commit messages so you can see who did what. It doesn't really matter how you're tracking it, as long as you can somehow prove your value whenever someone questions you about your work. Note that managers usually have a decent idea of which team members are productive and who is slacking off, even if they don't mention anything about it.
The value of informal communication
Do not underestimate the value of informal chatting during work hours. I fully agree that it's time not spent on getting actual work done. But what does it accomplish?
The number 1 positive aspect is getting along with other coworkers. If you're in a habit of chatting with certain coworkers, you're also much more likely to ask a quick work related question. Especially for new hires it can be a difficult thing to ask a coworker a question that maybe "they should have known already". If they're already on good terms with coworkers because of the daily chatting, it really lowers the threshold and the question actually get's asked.
These informal channels are even far more important if they happen in between different teams. I've had plenty of times where someone in my "chat group" at work was complaining about some issue they had, where someone from a different team could point them to another coworker that is an expert on that topic. Without the informal channel, the former would have wasted a lot of time trying to figure it out themselves.
Another positive point is that some people need some time to "get in the right work mood" as other answers here have already pointed out. Some people are just slow to get started and almost nobody is able to really focus 100% for 7 hours in a workday. Which would be worse, someone staring braindead to their screen getting about 2 hours of work actually done that day OR that same person chatting for an hour to get started, get those 2 hours done before noon and do something similar in the afternoon for a nice 5 hours of effective work done?
Solutions for you
There are 3 main "solutions" that I can think of for your situation.
1) Ignore them and hope for a raise because you're obviously the most valuable employee.
If those chatty coworkers are really not pulling their weight, then their manager will (/should) at some point do something about it. (Worse case for them is firing, best case a small reprimanding and a joint solution proposal to make the entire team more productive). This solution assumes you can acknowledge that you really are not responsible at all.
2) Make them aware that they're waisting too much time.
Let them have their 20 minutes chat in the morning, you might even join in at times to get on good terms with them as well (see advantages mentioned earlier). Every once in a while when they're chatting too long (30 mins +) and it didn't switch to work related topics you can point it out or break the conversation with a question. Depending on how often they do it, and how friendly you are with them (known to be a joker yourself or super serious ...) there's a couple of options:
- "You guys didn't learn about work ethics at school or what?" (try friendly tone when they've been chatting for about an hour).
- "Hey [talker 1], how's [issue you know is assigned to them] going? (optional extra:) Do you need help getting started?" (Really useful if you are somewhat responsible of sharing knowledge with new colleagues).
- "Ahum! *clears throat, looks at them expectedly"
- "Hey [either one of the talkers], what time is it?"
- "Oh sure, I'll do all the work here so you guys can have your little tea party over there. Did you make sure to bring cookies this time?" (be careful with jokes like this, if you can't also use the right body language to make it clear it's a joke it will make them really anoyed with you).
The idea is to give them (hopefully) friendly reminders that they're expected to be working. As a senior member of the team it's your job to show them the "business culture". You can tell them how "things are done around here" even if you cannot enforce it directly. Make sure not to just be the "grumpy old guy" that they want to ignore though. Try to earn their respect by showing how to get work done and help them if they're stuck.
3) Start doing daily standup meetings in the morning like Kiril suggested.
Get some buy in from your manager (or just agree with the entire team) that it's a good idea to start the day with a daily standup so everyone has at least some idea what everyone else is working on. That way, you "force" them to at least consider what needs to be done that day so they get into the right work-mind doing something more productive for the entire team than chatting about non-work stuff. Note that this does imply everyone is in on the standup, so you also "lose" that time if you don't consider it useful yourself. (Small tips: make sure nobody talks for more than 5 minutes during this standup. It should really be a really quick "I'm planning doing foo and bar issues today but I need to find out how to fix that bug on baz issue from yesterday first". (<- someone might suggest looking along with them after the standup, don't go into the issue at that point yet!).